Dragan V., Morozan T., Stoica A.M. Mathematical Methods in Robust Control of Linear Stochastic Systems

2nd edition. — Springer, 2013. — 455 p.This monograph presents a thorough description of the mathematical theory of robust linear stochastic control systems. The interest in this topic is motivated by the variety of random phenomena arising in physical, engineering, biological, and social processes. The study of stochastic systems has a long history, but two distinct classes of such systems drew much attention in the control literature, namely stochastic systems subjected to white noise perturbations and systems with Markovian jumping. At the same time, the remarkable progress in recent decades in the control theory of deterministic dynamic systems strongly influenced the research effort in the stochastic area. Thus, the modem treatments of stochastic systems include optimal control, robust stabilization, and H2-and H∞-type results for both stochastic systems corrupted with white noise and systems with jump Markov perturbations.
In this context, there are two main objectives of the present book. The first one is to develop a mathematical theory linear time-varying stochastic systems including both white noise jump Markov perturbations. From the perspective of this generalized theory the stochastic systems subjected only to white noise perturbations or to jump Markov perturbations can be regarded as particular cases. The second objective is to develop analysis and design methods for advanced control problems of linear stochastic systems with white noise and Markovianjumping as linearquadratic control, robust stabilization, and disturbance attenuation problems. Taking into account the maj or role played by the Riccati equations in these problems, the book presents this type of equation in a general framework. Particular attention is paid to the numerical aspects arising in the control problems of stochastic systems; new numerical algorithms to solve coupled matrix algebraic Riccati equations are also proposed and illustrated by numerical examples.