Introduction -- Chapter 1. Stochastic Processes - Introduction -- Chapter 2. Stochastic Systems -- Chapter 3. Stochastic Realization - Gaussian Systems -- Chapter 4. Stochastic Realization - General Framework -- Chapter 5. Stochastic Control Systems -- Chapter 6. Stochastic Control - Problems -- Chapter 7. Stochastic Control - Complete Observations - Finite Horizon -- Chapter 8. Stochastic Control - Complete Observations - Infinite Horizon -- Chapter 9. Stochastic Control - General Theory -- Chapter 10. Filtering - Kalman Filters -- Chapter 11. Filtering - General Stochastic Systems -- Chapter 12. Stochastic Control - Partial Observations - Finite Horizon -- Chapter 13. Stochastic Control - Partial Observations - Infinite Horizon -- Chapter 14. The Communication of Information -- Chapter 15. Mathematics - Notation, Concepts, and Results -- Chapter 16. Probability - Further Theory -- Chapter 17. Stochastic Processes - Specialized Topics -- Chapter 18. Deterministic Dynamic Systems -- Chapter 19. The Lyapunov and the Riccati Systems and Their Equations -- Chapter 20. Dissipative Systems -- Chapter 21. The Dissipation Matrix Inequality.

This book helps students, researchers, and practicing engineers to understand the theoretical framework of control and system theory for discrete-time stochastic systems so that they can then apply its principles to their own stochastic control systems and to the solution of control, filtering, and realization problems for such systems. Applications of the theory in the book include the control of ships, shock absorbers, traffic and communications networks, and power systems with fluctuating power flows. The focus of the book is a stochastic control system defined for a spectrum of probability distributions including Bernoulli, finite, Poisson, beta, gamma, and Gaussian distributions. The concepts of observability and controllability of a stochastic control system are defined and characterized. Each output process considered is, with respect to conditions, represented by a stochastic system called a stochastic realization. The existence of a control law is related to stochastic controllability while the existence of a filter system is related to stochastic observability. Stochastic control with partial observations is based on the existence of a stochastic realization of the filtration of the observed process.