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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.

Discrete-time systems -- Mathematical models. --- Linear systems -- Mathematical models. --- Robust control -- Mathematical models. --- Stochastic systems -- Mathematical models. --- Robust control --- Discrete-time systems --- Linear systems --- Stochastic systems --- Mathematical models. --- Systems, Stochastic --- Systems, Linear --- DES (System analysis) --- Discrete event systems --- Sampled-data systems --- Robustness (Control systems) --- Mathematics. --- Applied mathematics. --- Engineering mathematics. --- System theory. --- Numerical analysis. --- Mathematical optimization. --- Probabilities. --- Robotics. --- Automation. --- Applications of Mathematics. --- Robotics and Automation. --- Probability Theory and Stochastic Processes. --- Systems Theory, Control. --- Optimization. --- Numerical Analysis. --- Stochastic processes --- System analysis --- Differential equations, Linear --- System theory --- Digital control systems --- Linear time invariant systems --- Automatic control --- Distribution (Probability theory. --- Systems theory. --- Mathematical analysis --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Maxima and minima --- Operations research --- Simulation methods --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Math --- Science --- Automatic factories --- Automatic production --- Computer control --- Engineering cybernetics --- Factories --- Industrial engineering --- Mechanization --- Assembly-line methods --- Automatic machinery --- CAD/CAM systems --- Robotics --- Automation --- Machine theory --- Systems, Theory of --- Systems science --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Engineering --- Engineering analysis --- Philosophy