Mathematical Methods in Robust Control of Linear Stochastic Systems

Preliminaries to Probability Theory and Stochastic Differential Equations.- Exponential Stability and Lyapunov-Type Linear Equations.- Structural Properties of Linear Stochastic Systems.- The Riccati Equations of Stochastic Control.- Linear Quadratic Control Problem for Linear Stochastic Systems.- Stochastic Version of the Bounded Real Lemma and Applications.- Robust Stabilization of Linear Stochastic Systems.

Linear stochastic systems are successfully used to provide mathematical models for real processes in fields such as aerospace engineering, communications, manuafacturing, finance and economy. This monograph presents a useful methodology for the control of such stochastic systems, with both multiplicative white noise and Markovian jumping. An important feature is the inclusion of the necessary pre-requisites from probability theory, stochastic processes, stochastic integrals and stochastic differential equations. The systematic style of presentation leads the reader in a natural way to the original results. This unique monograph is geared to researchers and graduate students in advanced control engineering, mathematical systems theory and finance, numerical analysis. It is also accessible to undergraduate students with a fundamental knowledge of the theory of stochastic systems.

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)