Analysis of Periodically Time-Varying Systems

Many of the practical techniques developed for treating systems described by periodic differential equations have arisen in different fields of application; con sequently some procedures have not always been known to workers in areas that might benefit substantially from them. Furthermore, recent analytical methods are computationally based so that it now seems an opportune time for an applications-oriented book to be made available that, in a sense, bridges the fields in which equations with periodic coefficients arise and which draws together analytical methods that are implemented readily. This book seeks to ftll that role, from a user's and not a theoretician's view. The complexities of periodic systems often demand a computational approach. Matrix treatments therefore are emphasized here although algebraic methods have been included where they are useful in their own right or where they establish properties that can be exploited by the matrix approach. The matrix development given calls upon the nomenclature and treatment of H. D'Angelo, Linear Time Varying Systems: Analysis and Synthesis (Boston: Allyn and Bacon 1970) which deals with time-varying systems in general. It is recommended for its modernity and comprehensive approach to systems analysis by matrix methods. Since the present work is applications-oriented no attempt has been made to be complete theoretically by way of presenting all proofs, existence theorems and so on. These can be found in D'Angelo and classic and well-developed treatises such as McLachlan, N. W. : Theory and application of Mathieu functions.

Autorentext

John Richards has been active in remote sensing teaching and research for the past 40 years, mainly in image analysis and imaging radar. He is the author of four books, all published by Springer. He is an electrical engineering graduate from the University of New South Wales, Australia, and a life Fellow of the IEEE. He was the foundation director of the Centre for Remote Sensing at the University of New South Wales in the 1980s and has had a career that has taken him through teaching and research in remote sensing and engineering. He has also served in senior academic administration including as dean of the College of Engineering and Computer Science and vice-president of the Australian National University. He is an emeritus professor of both the Australian National University and the University of New South Wales.

Inhalt
Part-I Theory and Techniques.- 1 Historical Perspective.- 2 The Equations and Their Properties.- 3 Solutions to Periodic Differential Equations.- 4 Stability.- 5 A Modelling Technique for Hill Equations.- 6 The Mathieu Equation.- II Applications.- 7 Practical Periodically Variable Systems.- Appendix Bessel Function Generation by Chebyshev Polynomial Methods.- References for Appendix.