Control Engineering – serie

The twenty-one invited chapters in this book are an outgrowth of a workshop to honor Anthony N. Michel on the occasion of his retirement. The workshop provided a venue for researchers, colleagues, friends, and students to pay tribute to Michel's significant contributions to the systems and control community; at the same time, the workshop also served as a forum to explore topics and applications related to the stability and control of dynamical systems.His work is characterized both by great depth, as exemplified by his contributions to stability theory of dynamical systems, and by great breadth, as demonstrated by the wide range of problems he has addressed.The chapters are thematically organized into three main areas related to Michel's work. Part 1 contains seven chapters examining issues in stability analysis of dynamical systems; Part 2 includes six chapters dealing with artificial neural networks and signal processing; Part 3 contains eight chapters treating power systems and control systems.

Thishandbookwasmotivatedinpartbyourexperience(andthatofothers)in performing research and in teaching about networked and embedded control systems (NECS) as well as in implementing such systems. Although NECS— along with the technologies that enable them—have become ubiquitous, there are few, if any, sources where a student, researcher, or developer can gain a su?ciently broad view of the subject. Oftentimes, the needed information is scattered in articles, websites, and speci?cation sheets. Such di?culties are perhaps to be expected, given the relative newness of the subject and the diversity of its constitutive disciplines. From control theory and communi- tions, to computer science and electronics, the variety of approaches, tools, and language used by experts in each ?eld often acts as a barrier to und- standing how ideas ?t within the broader context of networked and embedded control. With the above in mind, we have gathered a collection of articles that provide at least an introduction to the important results, tools, software, and technologies that shape the area of NECS. Our goal was to present the most important knowledge about NECS in a book that would be useful to anyone who wants to learn about any aspect of the subject. We hope that we have succeeded and that every reader will ?nd valuable information in the book. Wethanktheauthorsofeachofthechapters. Theyareallbusypeopleand we are extremely grateful to them for their outstanding work.

Structural properties play an important role in our understanding of linear systems in the state space representation. The structural canonical form representation of linear systems not only reveals the structural properties but also facilitates the design of feedback laws that meet various control objectives. In particular, it decomposes the system into various subsystems. These subsystems, along with the interconnections that exist among them, clearly show the structural properties of the system. The simplicity of the subsystems and their explicit interconnections with each other lead us to a deeper insight into how feedback control would take effect on the system, and thus to the explicit construction of feedback laws that meet our design specifications. The discovery of structural canonical forms and their applications in feedback design for various performance specifications has been an active area of research for a long time. The effectiveness of the structural decomposition approach has also been extensively explored in nonlinear systems and control theory in the recent past. The aim of this book is to systematically present various canonical represen­ tations of the linear system, that explicitly reveal different structural properties of the system, and to report on some recent developments on its utilization in sys­ tem analysis and design.

Stochastic switching systems represent an interesting class of systems that can be used to model a variety of systems having abrupt random changes in their dynamics. Such systems may be found in the fields of manufacturing, communications, aerospace, power, and economics.This work presents stochastic switching systems and provides up-to-date methods and techniques for the analysis and design of various control systems with or without uncertainties. An introductory chapter highlights basic concepts and practical models, which are then used to solve more advanced problems throughout the book. Included are many numerical examples as well as LMI analysis methods and design approaches to supplement the developed results.Stochastic Switching Systems may be used as a supplementary textbook for graduate-level engineering courses, or as a reference for control engineers, graduate students, and researchers in systems and control. Prerequisites include elementary courses in matrix theory, probability, optimization techniques, and control systems theory.

The design of nonlinear controllers for mechanical systems has been an ex­ tremely active area of research in the last two decades. From a theoretical point of view, this attention can be attributed to their interesting dynamic behavior, which makes them suitable benchmarks for nonlinear control the­ oreticians. On the other hand, recent technological advances have produced many real-world engineering applications that require the automatic con­ trol of mechanical systems. the mechanism for de­ Often, Lyapunov-based techniques are utilized as veloping different nonlinear control structures for mechanical systems. The allure of the Lyapunov-based framework for mechanical system control de­ sign can most likely be assigned to the fact that Lyapunov function candi­ dates can often be crafted from physical insight into the mechanics of the system. That is, despite the nonlinearities, couplings, and/or the flexible effects associated with the system, Lyapunov-based techniques can often be used to analyze the stability of the closed-loop system by using an energy­ like function as the Lyapunov function candidate. In practice, the design procedure often tends to be an iterative process that results in the death of many trees. That is, the controller and energy-like function are often constructed in concert to foster an advantageous stability property and/or robustness property. Fortunately, over the last 15 years, many system the­ ory and control researchers have labored in this area to produce various design tools that can be applied in a variety of situations.

The Kalman Filter gives an optimal estimate of the state of the given process based on output measurements. The aim of this text is to cover the theory of robust state estimation for the case in which the process model contains significant uncertainties and non-linearities.

Hybrid dynamical systems, both continuous and discrete dynamics and variables, have attracted considerable interest recently. This emerging area is found at the interface of control theory and computer engineering, focusing on the analogue and digital aspects of systems and devices. They are essential for advances in modern digital- controller technology. "Qualitative Theory of Hybrid Dynamical Systems" provides a thorough development and systematic presentation of the foundations and framework for hybrid dynamical systems. The presentation offers an accessible, but precise, development of the mathematical models, conditions for existence of limit cycles, and criteria of their stability. The book largely concentrates on the case of discretely controlled continuous-time systems and their relevance for modeling aspects of flexible manufacturing systems and dynamically routed queuing networks. Features and topics: *differential automata*development and use of the concept "cyclic linear differential automata" (CLDA)*switched single-server flow networks coverage*application to specific models of manufacturing systems and queuing networks*select collection of open problems for the subject*self-contained presentation of topics, with the necessary background This new book is an excellent resource for the study and analysis of hybrid dynamical systems used in systems and control engineering. Researchers, postgraduates and professionals in control engineering and computer engineering will find the book an up-to-date development of the relevant new concepts and tools.

During the past decade we have had to confront a series of control design prob­ lems - involving, primarily, multibody electro-mechanical systems - in which nonlinearity plays an essential role. Fortunately, the geometric theory of non­ linear control system analysis progressed substantially during the 1980s and 90s, providing crucial conceptual tools that addressed many of our needs. However, as any control systems engineer can attest, issues of modeling, computation, and implementation quickly become the dominant concerns in practice. The prob­ lems of interest to us present unique challenges because of the need to build and manipulate complex mathematical models for both the plant and controller. As a result, along with colleagues and students, we set out to develop computer algebra tools to facilitate model building, nonlinear control system design, and code generation, the latter for both numerical simulation and real time con­ an outgrowth of that continuing effort. As trol implementation. This book is a result, the unique features of the book includes an integrated treatment of nonlinear control and analytical mechanics and a set of symbolic computing software tools for modeling and control system design. By simultaneously considering both mechanics and control we achieve a fuller appreciation of the underlying geometric ideas and constructions that are common to both. Control theory has had a fruitful association with analytical mechanics from its birth in the late 19th century.

Dynamics systems (living organisms, electromechanical and industrial systems, chemical and technological processes, market and ecology, and so forth) can be considered and analyzed using information and systems theories. For example, adaptive human behavior can be studied using automatic feedback control. As an illustrative example, the driver controls a car changing the speed and steer­ ing wheels using incoming information, such as traffic and road conditions. This book focuses on the most important and manageable topics in applied multivariable control with application to a wide class of electromechanical dynamic systems. A large spectrum of systems, familiar to electrical, mechanical, and aerospace stu­ dents, engineers, and scholars, are thoroughly studied to build the bridge between theory and practice as well as to illustrate the practical application of control theory through illustrative examples. It is the author's goal to write a book that can be used to teach undergraduate and graduate classes in automatic control and nonlin­ ear control at electrical, mechanical, and aerospace engineering departments. The book is also addressed to engineers and scholars, and the examples considered allow one to implement the theory in a great variety of industrial systems. The main purpose of this book is to help the reader grasp the nature and significance of multivariable control.

This monograph is a self-contained, coherent presentation of the background and progress of the stability of time-delay systems. Focusing on techniques, tools, and advances in numerical methods and optimization algorithms, the authors developed material which, up until now, has been scattered in technical journals and conference proceedings. Special emphasis is placed on systems with uncertainty and stability criteria which can be computationally implemented.  The second edition is major update to reflect the state of art in this field greatly expanding on the original material in addition to two new chapters on Systems of Neutral Type and an Introduction to Frequency Domain Method. Requiring only basic knowledge of linear systems and Lyapunov stability theory, Stability of Time-Delay Systems, 2nd ed is accessible to a broad audience of researchers, professional engineers, and graduate students. It may be used for self-study or as a reference; portions of the text may be used in advanced graduate courses and seminars.

Saturation nonlinearities are ubiquitous in engineering systems. In control systems, every physical actuator or sensor is subject to saturation owing to its maximum and minimum limits. A digital filter is subject to saturation if it is implemented in a finite word length format. Saturation nonlinearities are also purposely introduced into engineering systems such as control sys­ tems and neural network systems. Regardless of how saturation arises, the analysis and design of a system that contains saturation nonlinearities is an important problem. Not only is this problem theoretically challenging, but it is also practically imperative. This book intends to study control systems with actuator saturation in a systematic way. It will also present some related results on systems with state saturation or sensor saturation. Roughly speaking, there are two strategies for dealing with actuator sat­ uration. The first strategy is to neglect the saturation in the first stage of the control design process, and then to add some problem-specific schemes to deal with the adverse effects caused by saturation. These schemes, known as anti-windup schemes, are typically introduced using ad hoc modifications and extensive simulations. The basic idea behind these schemes is to intro­ duce additional feedbacks in such a way that the actuator stays properly within its limits. Most of these schemes lead to improved performance but poorly understood stability properties.

This book is primarily a research monograph that presents in a unified man­ ner some recent research on a class of hybrid dynamical systems (HDS). The book is intended both for researchers and advanced postgraduate stu­ dents working in the areas of control engineering, theoretical computer science, or applied mathematics and with an interest in the emerging field of hybrid dynamical systems. The book assumes competence in the basic mathematical techniques of modern control theory. The material presented in this book derives from a period of fruitful research collaboration between the authors that began in 1994 and is still ongoing. Some of the material contained herein has appeared as isolated results in journal papers and conference proceedings. This work presents this material in an integrated and coherent manner and also presents many new results. Much of the material arose from joint work with students and colleagues, and the authors wish to acknowledge the major contributions made by Ian Petersen, Efstratios Skafidas, Valery Ugrinovskii, David Cook, Iven Mareels, and Bill Moran. There is currently no precise definition of a hybrid dynamical system; however, in broad terms it is a dynamical system that involves a mixture of discrete-valued and continuous-valued variables. Since the early 1990s, a bewildering array of results have appeared under the umbrella of HDS, ranging from the analysis of elementary on-off control systems to sophis­ ticated mathematical logic-based descriptions of large real-time software systems.

Deterministic and Stochastic Time-Delay Systems provides professionals and advanced students in control engineering with the most recent results on deterministic and stochastic time-delay systems. It is an excellent text/reference for graduate level engineering students, or a reference for practicing control engineers, and researchers in control engineering. The control of uncertain systems has dominated the research effort of the control community during the last two decades. Some practical dynamical systems have time-delay in their dynamics, which makes their control a complicated task even in the deterministic case. The presence of time-delay in dynamical systems is a well-known case of instability and preference degradation.

Recent advancements in Lyapunov-based design and analysis techniques have applications to a broad class of engineering systems, including mechanical, electrical, robotic, aerospace, and underactuated systems. This book provides a practical yet rigorous development of nonlinear, Lyapunov-based tools and their use in the solution of control-theoretic problems. Rich in motivating examples and new design techniques, the text balances theoretical foundations and real-world implementation. Features include: * Control designs for a broad class of engineering systems * Presentation of adaptive and learning control methods for uncertain nonlinear systems * Experimental testbed descriptions and results that guide the reader toward techniques for further research * Development of necessary mathematical background in each chapter; additional mathematical prerequisites contained in two appendices Intended for readers who have some knowledge of undergraduate systems theory, the book includes a wide range of applications making it suitable for an extensive audience. Graduate students and researchers in control systems, robotics, and applied mathematics, as well as professional engineers will appreciate the work's combination of theoretical underpinnings and current and emerging engineering applications.

This monograph presents our recent results on the proportional-integr- derivative (PID) controller and its design, analysis, and synthesis. The fo­ cus is on linear time-invariant plants that may contain a time delay in the feedback loop. This setting captures many real-world practical and in­ dustrial situations. The results given here include and complement those published in Structure and Synthesis of PID Controllers by Datta, Ho, and Bhattacharyya [10]. In [10] we mainly dealt with the delay-free case. The main contribution described here is the efficient computation of the entire set of PID controllers achieving stability and various performance specifications. The performance specifications that can be handled within our machinery are classical ones such as gain and phase margin as well as modern ones such as Hoo norms of closed-loop transfer functions. Finding the entire set is the key enabling step to realistic design with several design criteria. The computation is efficient because it reduces most often to lin­ ear programming with a sweeping parameter, which is typically the propor­ tional gain. This is achieved by developing some preliminary results on root counting, which generalize the classical Hermite-Biehler Theorem, and also by exploiting some fundamental results of Pontryagin on quasi-polynomials to extract useful information for controller synthesis. The efficiency is im­ portant for developing software design packages, which we are sure will be forthcoming in the near future, as well as the development of further capabilities such as adaptive PID design and online implementation.

Fuzzy logic methodology has been proven effective in dealing with complex nonlinear systems containing uncertainties that are otherwise difficult to model. Technology based on this methodology has been applied to many real-world problems, especially in the area of consumer products. This book presents the first unified and thorough treatment of fuzzy modeling and fuzzy control, providing necessary tools for the control of complex nonlinear systems. Careful consideration is given to questions concerning model complexity, model precision, and computing time.In addition to being an excellent reference for electrical, computer, chemical, industrial, civil, manufacturing, mechanical and aeronautical engineers, the book may also be appropriate for classroom use in a graduate course in electrical engineering, computer engineering, and computer science. Applied mathematicians, control engineers, computer scientists, and physicists will benefit from the presentation as well.

Although there is an emerging literature on the topic, this is the first book that attempts to present a systematic theory of estimation and control over communication networks. Using several selected problems of estimation and control over communication networks, the authors present and prove a number of results concerning optimality, stability, and robustness having practical significance for networked control system design. In particular, various problems of Kalman filtering, stabilization, and optimal control over communication channels are considered and solved. The results establish fundamental links among mathematical control theory, Shannon information theory, and entropy theory of dynamical systems.This essentially self-contained monograph offers accessible mathematical models and results for advanced postgraduate students, researchers, and practitioners working in the areas of control engineering, communications, information theory, signal processing, and applied mathematics.

This monograph explores a consistent modeling and analytic framework that provides the tools for an improved understanding of the behavior and the building of efficient models of power systems.  It covers the essential concepts for the study of static and dynamic network stability, reviews the structure and design of basic voltage and load-frequency regulators, and offers an introduction to power system optimal control with reliability constraints.  A set of Mathematica tutorial notebooks providing detailed solutions of the examples worked-out in the text, as well as a package that will enable readers to work out their own examples and problems, supplements the text.A key premise of the book is that the design of successful control systems requires a deep understanding of the processes to be controlled; as such, the technical discussion begins with a concise review of the physical foundations of electricity and magnetism.  This is followed by an overview of nonlinear circuits that include resistors, inductors, capacitors, and memristors, along with an examination of basic circuit mathematical models and formulations.  AC power systems are considered next, in which models for their basic components are derived.  The following chapters address power system dynamics using both the ordinary differential equation and differential-algebraic equation models of a power network, as well as bifurcation analysis and the behavior of a network as it approaches voltage instability.  Two classic control problems – voltage regulation and load-frequency control – are then described, including the coordination of economic dispatch with load-frequency control.  Finally, power system control problems involving operation in highly nonlinear regimes and subjected to discrete failure modes are discussed.Power System Dynamics and Control will appeal to practicing power system engineers, control systems engineers interested in powersystems, and graduate students in these areas.  Because it provides sufficient information about their modelling and behavior, control engineers without a background in power systems will also find it to be a valuable resource.

This book-the first of its kind-presents general methods for feedback controller synthesis and optimization of multiscale systems, illustrating their application to thin-film growth, sputtering processes, and catalytic systems of industrial interest. The authors demonstrate the advantages of the methods presented for control and optimization through extensive simulations. Included in the work are new techniques for feedback controller design and optimization of multiscale process systems that are not included in other books. The book also contains a rich collection of new research topics and references to significant recent work.

Automatic Control of Atmospheric and Space Flight Vehicles  is perhaps the first book on the market to present a unified and straightforward study of the design and analysis of automatic control systems for both atmospheric and space flight vehicles. Covering basic control theory and design concepts, it is meant as a textbook for senior undergraduate and graduate students in modern courses on flight control systems. In addition to the basics of flight control, this book covers a number of upper-level topics and will therefore be of interest not only to advanced students, but also to researchers and practitioners in aeronautical engineering, applied mathematics, and systems/control theory.

The sliding mode control methodology has proven effective in dealing with complex dynamical systems affected by disturbances, uncertainties and unmodeled dynamics. Robust control technology based on this methodology has been applied to many real-world problems, especially in the areas of aerospace control, electric power systems, electromechanical systems, and robotics. Sliding Mode Control and Observation represents the first textbook that starts with classical sliding mode control techniques and progresses toward newly developed higher-order sliding mode control and observation algorithms and their applications.The present volume addresses a range of sliding mode control issues, including:*Conventional sliding mode controller and observer design*Second-order sliding mode controllers and differentiators*Frequency domain analysis of conventional and second-order sliding mode controllers*Higher-order sliding mode controllers and differentiators*Higher-order sliding mode observers *Sliding mode disturbance observer based control *Numerous applications, including reusable launch vehicle and satellite formation control, blood glucose regulation, and car steering control are used as case studiesSliding Mode Control and Observation is aimed at graduate students with a basic knowledge of classical control theory and some knowledge of state-space methods and nonlinear systems, while being of interest to a wider audience of graduate students in electrical/mechanical/aerospace engineering and applied mathematics, as well as researchers in electrical, computer, chemical, civil, mechanical, aeronautical, and industrial engineering, applied mathematicians, control engineers, and physicists. Sliding Mode Control and Observation provides the necessary tools for graduate students, researchers and engineers to robustly control complex and uncertain nonlinear dynamical systems. Exercises provided at the end of each chapter make this an ideal text for an advanced course taught in control theory.

Stability is one of the most studied issues in the theory of time-delay systems, however the corresponding chapters of published volumes on time-delay systems do not include a comprehensive study of a counterpart of classical Lyapunov theory for linear delay free systems. The principal goal of the book is to fill this gap, and to provide readers with a systematic and exhaustive treatment of the basic concepts of the Lyapunov-Krasovskii approach to the stability analysis of linear time-delay systems.​ Time-Delay Systems: Lyapunov Functionals and Matrices​ will be of great use and interest to researchers and graduate students in automatic control and applied mathematics as well as practicing engineers involved in control system design.​

Recent advancements in Lyapunov-based design and analysis techniques have applications to a broad class of engineering systems, including mechanical, electrical, robotic, aerospace, and underactuated systems. This book provides a practical yet rigorous development of nonlinear, Lyapunov-based tools and their use in the solution of control-theoretic problems. Rich in motivating examples and new design techniques, the text balances theoretical foundations and real-world implementation. Features include: * Control designs for a broad class of engineering systems * Presentation of adaptive and learning control methods for uncertain nonlinear systems * Experimental testbed descriptions and results that guide the reader toward techniques for further research * Development of necessary mathematical background in each chapter; additional mathematical prerequisites contained in two appendices Intended for readers who have some knowledge of undergraduate systems theory, the book includes a wide range of applications making it suitable for an extensive audience. Graduate students and researchers in control systems, robotics, and applied mathematics, as well as professional engineers will appreciate the work's combination of theoretical underpinnings and current and emerging engineering applications.

It is with great pleasure that I offer my reflections on Professor Anthony N. Michel's retirement from the University of Notre Dame. I have known Tony since 1984 when he joined the University of Notre Dame's faculty as Chair of the Depart­ ment of Electrical Engineering. Tony has had a long and outstanding career. As a researcher, he has made im­ portant contributions in several areas of systems theory and control theory, espe­ cially stability analysis of large-scale dynamical systems. The numerous awards he received from the professional societies, particularly the Institute of Electrical and Electronics Engineers (IEEE), are a testament to his accomplishments in research. He received the IEEE Control Systems Society's Best Transactions Paper Award (1978), and the IEEE Circuits and Systems Society's Guillemin-Cauer Prize Paper Award (1984) and Myril B. Reed Outstanding Paper Award (1993), among others. In addition, he was a Fulbright Scholar (1992) and received the Alexander von Hum­ boldt Forschungspreis (Alexander von Humboldt Research Award for Senior U.S. Scientists) from the German government (1997). To date, he has written eight books and published over 150 archival journal papers. Tony is also an effective administrator who inspires high academic standards.

This monograph is a self-contained, coherent presentation of the background and progress of the stability of time-delay systems. Focusing on techniques, tools, and advances in numerical methods and optimization algorithms, the authors developed material which, up until now, has been scattered in technical journals and conference proceedings. Special emphasis is placed on systems with uncertainty and stability criteria which can be computationally implemented.  The second edition is major update to reflect the state of art in this field greatly expanding on the original material in addition to two new chapters on Systems of Neutral Type and an Introduction to Frequency Domain Method. Requiring only basic knowledge of linear systems and Lyapunov stability theory, Stability of Time-Delay Systems, 2nd ed is accessible to a broad audience of researchers, professional engineers, and graduate students. It may be used for self-study or as a reference; portions of the text may be used in advanced graduate courses and seminars.

Most practical processes such as chemical reactor, industrial furnace, heat exchanger, etc., are nonlinear stochastic systems, which makes their con­ trol in general a hard problem. Currently, there is no successful design method for this class of systems in the literature. One common alterna­ tive consists of linearizing the nonlinear dynamical stochastic system in the neighborhood of an operating point and then using the techniques for linear systems to design the controller. The resulting model is in general an approximation of the real behavior of a dynamical system. The inclusion of the uncertainties in the model is therefore necessary and will certainly improve the performance of the dynamical system we want to control. The control of uncertain systems has attracted a lot of researchers from the control community. This topic has in fact dominated the research effort of the control community during the last two decades, and many contributions have been reported in the literature. Some practical dynamical systems have time delay in their dynamics, which makes their control a complicated task even in the deterministic case. Recently, the class ofuncertain dynamical deterministic systems with time delay has attracted some researchers, and some interesting results have been reported in both deterministic and stochastic cases. But wecan't claim that the control problem ofthis class ofsystems is completely solved; more work must be done for this class of systems.

This book is primarily a research monograph that presents in a unified man­ ner some recent research on a class of hybrid dynamical systems (HDS). The book is intended both for researchers and advanced postgraduate stu­ dents working in the areas of control engineering, theoretical computer science, or applied mathematics and with an interest in the emerging field of hybrid dynamical systems. The book assumes competence in the basic mathematical techniques of modern control theory. The material presented in this book derives from a period of fruitful research collaboration between the authors that began in 1994 and is still ongoing. Some of the material contained herein has appeared as isolated results in journal papers and conference proceedings. This work presents this material in an integrated and coherent manner and also presents many new results. Much of the material arose from joint work with students and colleagues, and the authors wish to acknowledge the major contributions made by Ian Petersen, Efstratios Skafidas, Valery Ugrinovskii, David Cook, Iven Mareels, and Bill Moran. There is currently no precise definition of a hybrid dynamical system; however, in broad terms it is a dynamical system that involves a mixture of discrete-valued and continuous-valued variables. Since the early 1990s, a bewildering array of results have appeared under the umbrella of HDS, ranging from the analysis of elementary on-off control systems to sophis­ ticated mathematical logic-based descriptions of large real-time software systems.

Dynamics systems (living organisms, electromechanical and industrial systems, chemical and technological processes, market and ecology, and so forth) can be considered and analyzed using information and systems theories. For example, adaptive human behavior can be studied using automatic feedback control. As an illustrative example, the driver controls a car changing the speed and steer­ ing wheels using incoming information, such as traffic and road conditions. This book focuses on the most important and manageable topics in applied multivariable control with application to a wide class of electromechanical dynamic systems. A large spectrum of systems, familiar to electrical, mechanical, and aerospace stu­ dents, engineers, and scholars, are thoroughly studied to build the bridge between theory and practice as well as to illustrate the practical application of control theory through illustrative examples. It is the author's goal to write a book that can be used to teach undergraduate and graduate classes in automatic control and nonlin­ ear control at electrical, mechanical, and aerospace engineering departments. The book is also addressed to engineers and scholars, and the examples considered allow one to implement the theory in a great variety of industrial systems. The main purpose of this book is to help the reader grasp the nature and significance of multivariable control.

Saturation nonlinearities are ubiquitous in engineering systems. In control systems, every physical actuator or sensor is subject to saturation owing to its maximum and minimum limits. A digital filter is subject to saturation if it is implemented in a finite word length format. Saturation nonlinearities are also purposely introduced into engineering systems such as control sys­ tems and neural network systems. Regardless of how saturation arises, the analysis and design of a system that contains saturation nonlinearities is an important problem. Not only is this problem theoretically challenging, but it is also practically imperative. This book intends to study control systems with actuator saturation in a systematic way. It will also present some related results on systems with state saturation or sensor saturation. Roughly speaking, there are two strategies for dealing with actuator sat­ uration. The first strategy is to neglect the saturation in the first stage of the control design process, and then to add some problem-specific schemes to deal with the adverse effects caused by saturation. These schemes, known as anti-windup schemes, are typically introduced using ad hoc modifications and extensive simulations. The basic idea behind these schemes is to intro­ duce additional feedbacks in such a way that the actuator stays properly within its limits. Most of these schemes lead to improved performance but poorly understood stability properties.