Overview

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.

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9781489984470

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Reviews

From the reviews: “This monograph deals with the control theory of linear discrete-time stochastic systems subject to multiplicative white noise and to Markov jumping, as arising in many engineering areas, such as communications, fault detection and isolation, robust control, stochastic filtering navigation as wells as in finance, economics and biology. … The theoretical developments are illustrated by several examples. … The book is suitable for advanced courses in robust control of discrete-time stochastic systems, where a good knowledge of probability theory and linear control systems is needed.” (Kurt Marti, Zentralblatt MATH, Vol. 1183, 2010) “The book is dedicated to control theory of linear discrete-time stochastic systems perturbed by both multiplicative white noise and Markov jumps. … The book is recommended to graduate students and researchers in the field of applied mathematics and stochastic control.”­­­ (Pavel Pakshin, Mathematical Reviews, Issue 2011 d)

From the reviews: The subject of the book is related to the development of a theory of linear stochastic systems including both white noise and jump Markov perturbations, and to the development of analysis and design methods for linear-quadratic control, robust stabilization and disturbance attenuation problems. The book addresses graduate students and researchers in advanced control engineering, applied mathematics, mathematical systems theory and finance. (Vladimir Sobolev, Zentralblatt MATH, Vol. 1101 (3), 2007) 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 disturbance attenuation. 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)

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