Vasile Dragan - Böcker

One of the main problems in control theory is the stabilization problem consisting of finding a feedback control law ensuring stability; when the linear approximation is considered, the nat­ ural problem is stabilization of a linear system by linear state feedback or by using a linear dynamic controller. This prob­ lem was intensively studied during the last decades and many important results have been obtained. The present monograph is based mainly on results obtained by the authors. It focuses on stabilization of systems with slow and fast motions, on stabilization procedures that use only poor information about the system (high-gain stabilization and adaptive stabilization), and also on discrete time implementa­ tion of the stabilizing procedures. These topics are important in many applications of stabilization theory. We hope that this monograph may illustrate the way in which mathematical theories do influence advanced technol­ ogy. This book is not intended to be a text book nor a guide for control-designers. In engineering practice, control-design is a very complex task in which stability is only one of the re­ quirements and many aspects and facets of the problem have to be taken into consideration. Even if we restrict ourselves to stabilization, the book does not provide just recipes, but it fo­ cuses more on the ideas lying behind the recipes. In short, this is not a book on control, but on some mathematics of control.

In this monograph the authors develop a theory for the robust control of discrete-time stochastic systems, subjected to both independent random perturbations and to Markov chains. Such systems are widely used to provide mathematical models for real processes in fields such as aerospace engineering, communications, manufacturing, finance and economy. The theory is a continuation of the authors’ work presented in their previous book entitled "Mathematical Methods in Robust Control of Linear Stochastic Systems" published by Springer in 2006.Key features:- Provides a common unifying framework for discrete-time stochastic systems corrupted with both independent random perturbations and with Markovian jumps which are usually treated separately in the control literature;- Covers preliminary material on probability theory, independent random variables, conditional expectation and Markov chains;- Proposes new numerical algorithms to solve coupled matrix algebraic Riccati equations;- Leads the reader in a natural way to the original results through a systematic presentation;- Presents new theoretical results with detailed numerical examples.The monograph is geared to researchers and graduate students in advanced control engineering, applied mathematics, mathematical systems theory and finance. It is also accessible to undergraduate students with a fundamental knowledge in the theory of stochastic systems.

Linear stochastic systems are successfully used to provide mathematical models for real processes in fields such as aerospace engineering, communications, manufacturing, finance and economy. This monograph presents a useful methodology for the control of such stochastic systems with a focus on robust stabilization in the mean square, linear quadratic control, the disturbance attenuation problem, and robust stabilization with respect to dynamic and parametric uncertainty. Systems with both multiplicative white noise and Markovian jumping are covered.Key Features:-Covers the necessary pre-requisites from probability theory, stochastic processes, stochastic integrals and stochastic differential equations-Includes detailed treatment of the fundamental properties of stochastic systems subjected both to multiplicative white noise and to jump Markovian perturbations-Systematic presentation leads the reader in a natural way to the original results-New theoretical results accompanied by detailed numerical examples-Proposes new numerical algorithms to solve coupled matrix algebraic Riccati equations.The unique monograph is geared to researchers and graduate students in advanced control engineering, applied mathematics, mathematical systems theory and finance. It is also accessible to undergraduate students with a fundamental knowledge in the theory of stochastic systems.

One of the main problems in control theory is the stabilization problem consisting of finding a feedback control law ensuring stability;

This second edition of Mathematical Methods in the Robust Control of Linear Stochastic Systems includes a large number of recent results in the control of linear stochastic systems. More specifically, the new results presented are:- A unified and abstract framework for Riccati type equations arising in the stochastic control- Stability and control problems for systems perturbed by homogeneous Markov processes with infinite number of states- Mixed H2 / H∞ control problem and numerical procedures- Linear differential equations with positive evolution on ordered Banach spaces with applications for stochastic systems including both multiplicative white noise and Markovian jumps represented by a Markov chain with countable infinite set of states-  Kalman filtering for stochastic systems subject both to state dependent noise and Markovian jumps-  H∞ reduced order filters for stochastic systemsThe book will appeal to graduate students, researchers in advanced control engineering, finance, mathematical systems theory, applied probability and stochastic processes, and numerical analysis.From Reviews of the First Edition:This book is concerned with robust control of stochastic systems. One of the main features is its coverage of jump Markovian systems. … Overall, this book presents results taking into consideration both white noise and Markov chain perturbations. It is clearly written and should be useful for people working in applied mathematics and in control and systems theory. The references cited provide further reading sources.(George Yin, Mathematical Reviews, Issue 2007 m)This book considers linear time varying stochastic systems, subjected to white noise disturbances and system parameter Markovian jumping, in the context of optimal control … robust stabilization, and disturbanceattenuation. … The material presented in the book is organized in seven chapters. … The book is very well written and organized. … is a valuable reference for all researchers and graduate students in applied mathematics and control engineering interested in linear stochastic time varying control systems with Markovian parameter jumping and white noise disturbances.(Zoran Gajic, SIAM Review, Vol. 49 (3), 2007)

In this monograph the authors develop a theory for the robust control of discrete-time stochastic systems, subjected to both independent random perturbations and to Markov chains. Such systems are widely used to provide mathematical models for real processes in fields such as aerospace engineering, communications, manufacturing, finance and economy. The theory is a continuation of the authors’ work presented in their previous book entitled "Mathematical Methods in Robust Control of Linear Stochastic Systems" published by Springer in 2006.Key features:- Provides a common unifying framework for discrete-time stochastic systems corrupted with both independent random perturbations and with Markovian jumps which are usually treated separately in the control literature;- Covers preliminary material on probability theory, independent random variables, conditional expectation and Markov chains;- Proposes new numerical algorithms to solve coupled matrix algebraic Riccati equations;- Leads the reader in a natural way to the original results through a systematic presentation;- Presents new theoretical results with detailed numerical examples.The monograph is geared to researchers and graduate students in advanced control engineering, applied mathematics, mathematical systems theory and finance. It is also accessible to undergraduate students with a fundamental knowledge in the theory of stochastic systems.

This second edition of Mathematical Methods in the Robust Control of Linear Stochastic Systems includes a large number of recent results in the control of linear stochastic systems. More specifically, the new results presented are:- A unified and abstract framework for Riccati type equations arising in the stochastic control- Stability and control problems for systems perturbed by homogeneous Markov processes with infinite number of states- Mixed H2 / H∞ control problem and numerical procedures- Linear differential equations with positive evolution on ordered Banach spaces with applications for stochastic systems including both multiplicative white noise and Markovian jumps represented by a Markov chain with countable infinite set of states-  Kalman filtering for stochastic systems subject both to state dependent noise and Markovian jumps-  H∞ reduced order filters for stochastic systemsThe book will appeal to graduate students, researchers in advanced control engineering, finance, mathematical systems theory, applied probability and stochastic processes, and numerical analysis.From Reviews of the First Edition:This book is concerned with robust control of stochastic systems. One of the main features is its coverage of jump Markovian systems. … Overall, this book presents results taking into consideration both white noise and Markov chain perturbations. It is clearly written and should be useful for people working in applied mathematics and in control and systems theory. The references cited provide further reading sources.(George Yin, Mathematical Reviews, Issue 2007 m)This book considers linear time varying stochastic systems, subjected to white noise disturbances and system parameter Markovian jumping, in the context of optimal control … robust stabilization, and disturbanceattenuation. … The material presented in the book is organized in seven chapters. … The book is very well written and organized. … is a valuable reference for all researchers and graduate students in applied mathematics and control engineering interested in linear stochastic time varying control systems with Markovian parameter jumping and white noise disturbances.(Zoran Gajic, SIAM Review, Vol. 49 (3), 2007)