Time-Varying Systems and Computations

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This text provides a detailed exposition of a unifying framework (developed by the authors) for the study of time-variant systems and the computational aspects and problems that arise in this context. While complex function theory and linear algebra provide much of the fundamental mathematics needed by engineers engaged in numerical computations, signal processing and/or control, there has long been a large, abstruse gap between the two fields. This book shows the reader how the gap between analysis and linear algebra can be bridged. In this monograph, the authors explore, discover and exploit many links that exist between classical linear algebraic concepts and complex analysis. The text attempts to open up perspectives on linear algebra from the analysis point of view. It explains a framework that allows the extension of classical results, from complex function theory to the case of time-variant operators and even finite-dimensional matrices. These results allow the user to obtain computationally feasible schemes and models for complex and large-scale systems. The volume should be of interest to a broad spectrum of researchers and professionals, including applied mathematicians, control theorists, systems theorists and numerical analysts. It can also be used as a graduate course in linear time-varying system theory.