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This book deals with algebraic criteria for root clustering (inclusion) in general regions in the complex plane. It is based on the view that there are three approaches to root clustering: composite matrices and polynomial symmetric matrices, and rational mappings. The book presents two main results of potential benefit to the reader. First, given a linear dynamical system, it is possible to analyze its relative stability. Second, for that system it is possible to construct a dynamic controller of fixed order for closed loop relative stability. The reader is assumed to have some knowledge of...

This book is concerned with dynamical systems under a large uncertainty, and uses a min-max approach to achieve worst-case design. The book consists of two parts. The first part deals with robust control. It begines by developing linear controls to achieve relative stability pole clustering under parameter uncertainty. Surprisingly, the largest robustness radius in the parameter space is sometimes discontinuous fragile with respect to the control parameters. Then, the book discusses the control of nonlinear uncertain systems under matching conditions. brThe second part uses differential games...