Elements of probability theory -- Discrete-time linear equations defined by positive operators -- Mean square exponential stability -- Structural properties of linear stochastic systems -- Discrete-time Riccati equations of stochastic control -- Linear quadratic optimization problems -- Discrete-time stochastic optimal control -- Robust stability and robust stabilization of discrete-time linear stochastic systems.

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.