This book helps students, researchers, and practicing engineers to understand the theoretical framework of control and system theory for discrete-time shastic systems so that they can then apply its principles to their own shastic 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 shastic 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 shastic control system are defined and characterized. Each output process considered is, with respect to conditions, represented by a shastic system called a shastic realization. The existence of a control law is related to shastic controllability while the existence of a filter system is related to shastic observability. Shastic control with partial observations is based on the existence of a shastic realization of the filtration of the observed process.​