This monograph is sums up the development of singular system theory and provides the control circle with a systematic theory of the system. It focuses on the analysis and synthesis of singular control systems. Its distinctive features include systematic discussion of controllabilities and observabilities, design of singular or normal observers and compensators with their structural stability, systems analysis via transfer matrix, and studies of discrete-time singular systems. Some acquaintance with linear algebra and linear systems is assumed. Prospective readers are graduate students, scientists, and other researchers in control theory and its applications. Much of the material in the book is new.

This book deals with the class of singular systems with random abrupt changes also known as singular Markovian jump systems. Various problems and their robustness are tackled. The book examines both the theoretical and practical aspects of the control problems from the angle of the structural properties of linear systems. It can be used as a textbook as well as a reference for researchers in control or mathematics with interest in control theory.

Singular systems have been widely studied in the past two decades due to their extensive applications in modelling and control of electrical circuits, power systems, economics and other areas. Interest has grown recently in the stability analysis and control of singular systems with parameter uncertainties due to their frequent presence in dynamic systems, which is much more complicated than that of state-space systems because controllers must be designed so that the closed-loop system is not only robustly stable, but also regular and impulse-free (in the continuous case) or causal (in the discrete case), while the latter two issues do not arise in the state-space case. This monograph aims to present up-to-date research developments and references on robust control and filtering of uncertain singular systems in a unified matrix inequality setting. It provides a coherent approach to studying control and filtering problems as extensions of state-space systems without the commonly used slow-fast decomposition. It contains valuable reference material for researchers wishing to explore the area of singular systems, and its contents are also suitable for a one-semester graduate course.

" ... the purpose of this book is to describe and analyse (and to some extent generalise) the principal results, scattered in the literature, concerning perturbation methods in optimal control for systems that are governed by deterministic or stochastic differential equations."--Preface.

Designed for one-semester introductory senior-or graduate-level course, the authors provide the student with an introduction of analysis techniques used in the design of nonlinear and optimal feedback control systems. There is special emphasis on the fundamental topics of stability, controllability, and optimality, and on the corresponding geometry associated with these topics. Each chapter contains several examples and a variety of exercises.