Abdellah Benzaouia - Böcker

Saturated Switching Systems treats the problem of actuator saturation, inherent in all dynamical systems by using two approaches: positive invariance in which the controller is designed to work within a region of non-saturating linear behaviour; and saturation technique which allows saturation but guarantees asymptotic stability.The results obtained are extended from the linear systems in which they were first developed to switching systems with uncertainties, 2D switching systems, switching systems with Markovian jumping and switching systems of the Takagi-Sugeno type.The text represents a thoroughly referenced distillation of results obtained in this field during the last decade. The selected tool for analysis and design of stabilizing controllers is based on multiple Lyapunov functions and linear matrix inequalities. All the results are illustrated with numerical examples and figures many of them being modelled using MATLAB®.Saturated Switching Systems will be of interest to academic researchers in control systems and to professionals working in any of the many fields where systems are affected by saturation including: chemical and pharmaceutical batch processing, manufacturing (for example in steel rolling), air-traffic control, and the automotive and aerospace industries.

This monograph puts the reader in touch with a decade’s worth of new developments in the field of fuzzy control specifically those of the popular Takagi-Sugeno (T-S) type. New techniques for stabilizing control analysis and design based on multiple Lyapunov functions and linear matrix inequalities (LMIs), are proposed. All the results are illustrated with numerical examples and figures and a rich bibliography is provided for further investigation.Control saturations are taken into account within the fuzzy model. The concept of positive invariance is used to obtain sufficient asymptotic stability conditions for the fuzzy system with constrained control inside a subset of the state space.The authors also consider the non-negativity of the states. This is of practical importance in many chemical, physical and biological processes that involve quantities that have intrinsically constant and non-negative sign: concentration of substances, level of liquids, etc. Results forlinear systems are then extended to linear systems with delay. It is shown that LMI techniques can usually handle the new constraint of non-negativity of the states when care is taken to use an adequate Lyapunov function. From these foundations, the following further problems are also treated: ·        asymptotic stabilization of uncertain T-S fuzzy systems with time-varying delay, focusing on delay-dependent stabilization synthesis based on parallel distributed controller (PDC);·        asymptotic stabilization of uncertain T-S fuzzy systems with multiple delays, focusing on delay-dependent stabilization synthesis based on PDC with results obtained under linear programming;·        design of delay-independent, observer-based, H-infinity control for T–S fuzzy systems with time varying delay; and·        asymptotic stabilization of 2-D T–S fuzzy systems.Advanced Takagi–Sugeno Fuzzy Systems provides researchers and graduate students interested in fuzzy control systems with further approaches based LMI and LP.

A solution permitting the stabilization of 2-dimensional (2-D) continuous-time saturated system under state feedback control is presented in this book. The problems of delay and saturation are treated at the same time. The authors obtain novel results on continuous 2-D systems using the unidirectional Lyapunov function. The control synthesis and the saturation and delay conditions are presented as linear matrix inequalities. Illustrative examples are worked through to show the effectiveness of the approach and many comparisons are made with existing results. The second half of the book moves on to consider robust stabilization and filtering of 2-D systems with particular consideration being given to 2-D fuzzy systems. Solutions for the filter-design problems are demonstrated by computer simulation. The text builds up to the development of state feedback control for 2-D Takagi–Sugeno systems with stochastic perturbation. Conservatism is reduced by using slack matrices and the coupling between the Lyapunov matrix and the system matrices is broken by using basis-dependent Lyapunov functions. Mean-square asymptotic stability and prescribed H-infinity performance are guaranteed.Two-Dimensional Systems emphasizes practical approaches to control and filter design under constraints that appear in real problems and uses off-the-shelf software to achieve its results. Researchers interested in control and filter design for multidimensional systems, especially multi-dimensional fuzzy systems, will find this book a useful resource as will graduate students specializing in dynamical sytems.

A solution permitting the stabilization of 2-dimensional (2-D) continuous-time saturated system under state feedback control is presented in this book. The second half of the book moves on to consider robust stabilization and filtering of 2-D systems with particular consideration being given to 2-D fuzzy systems.

This monograph puts the reader in touch with a decade’s worth of new developments in the field of fuzzy control specifically those of the popular Takagi-Sugeno (T-S) type. New techniques for stabilizing control analysis and design based on multiple Lyapunov functions and linear matrix inequalities (LMIs), are proposed. All the results are illustrated with numerical examples and figures and a rich bibliography is provided for further investigation.Control saturations are taken into account within the fuzzy model. The concept of positive invariance is used to obtain sufficient asymptotic stability conditions for the fuzzy system with constrained control inside a subset of the state space.The authors also consider the non-negativity of the states. This is of practical importance in many chemical, physical and biological processes that involve quantities that have intrinsically constant and non-negative sign: concentration of substances, level of liquids, etc. Results forlinear systems are then extended to linear systems with delay. It is shown that LMI techniques can usually handle the new constraint of non-negativity of the states when care is taken to use an adequate Lyapunov function. From these foundations, the following further problems are also treated: ·        asymptotic stabilization of uncertain T-S fuzzy systems with time-varying delay, focusing on delay-dependent stabilization synthesis based on parallel distributed controller (PDC);·        asymptotic stabilization of uncertain T-S fuzzy systems with multiple delays, focusing on delay-dependent stabilization synthesis based on PDC with results obtained under linear programming;·        design of delay-independent, observer-based, H-infinity control for T–S fuzzy systems with time varying delay; and·        asymptotic stabilization of 2-D T–S fuzzy systems.Advanced Takagi–Sugeno Fuzzy Systems provides researchers and graduate students interested in fuzzy control systems with further approaches based LMI and LP.

This book deals with a combination of two main problems for the first time. They are saturation on control and on the rate (or increment) of the control, and the solution of unsymmetrical saturation on the control by LMIs. It treats linear systems in state space form, in both the continuous- and discrete-time domains. Necessary and sufficient conditions are derived for autonomous linear systems with constrained state increment or rate, such that the system evolves respecting incremental or rate constraints if any. A pole assignment technique is then used to solve the problem, giving stabilizing state feedback controllers that respect non-symmetrical constraints on control alone or on both control and its increment or rate. Illustrative examples show the application of these methods on academic examples or on such real plant models as the double integrator system. This problem is then extended to various others including:systems with constraints and perturbations;singular systems with constrained control;systems with unsymmetrical saturations; saturated systems with delay, and2-D systems with saturations.The solutions obtained are of two types:necessary and sufficient conditions solved with linear programming techniques; andsufficient conditions under LMIs.A new approach extends existing techniques for dealing with symmetrical saturations to take direct account of unsymmetrical saturations into account with LMIs. This tool enables the authors to obtain new results on continuous- and discrete-time systems. The book uses illustrative examples and figures and provides many comparisons with existing results.Systems theoreticians interested in multidimensional systems and practitioners working with saturated and constrained controllers will find the research and background presented in Saturated Control of Linear Systems to be ofconsiderable interest in helping them overcome problems with their plant and in stimulating further research.