Root Clustering in Parameter Space

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 linear algebra and the theory of complex variables. The book is aimed at systems and control researchers, mathematicians and physicists. Introduction....Pages 1-8 Review of classical results....Pages 9-25 Introduction to root clustering....Pages 26-44 Transformable regions....Pages 45-68 Root clustering criteria....Pages 69-93 Symmetric matrix approach....Pages 94-117 Parameter space and feedback design....Pages 118-144