More and more digital devices are being used for informa­ tion processing and control purposes in a variety of systems applications, including industrial processes, power networks, biological systems and communication networks. This trend has been helped by the advent of microprocessors and the consequent availability of cheap distributed computing power. For those applications, where digital devices are used, it is reasonable to model the system in discrete-time. In addition there are other application areas, e.g. econometric systems, business systems, certain command and control systems, environmental systems, where the underlying models are in discrete-time and here discrete-time approaches to analysis and control are the most appropriate. In order to deal with these two situations, there has been a lot of interest in developing techLiques which allow us to do analysis, design and control of discrete-time systems. This book provides a comprehensive treatment of discrete­ time dynamical systems. It covers the topics of modelling, optimization techniques and control design. The book is designed to serve as a text for teaching at the first year graduate level. The material included is organized into eight chapters.