سیستم‌های بازخورد: ویژگی‌های ورودی-خروجی (علم الکتریکی)

This book was the first and remains the only book to give a comprehensive treatment of the behavior of linear or nonlinear systems when they are connected in a closed-loop fashion, with the output of one system forming the input of the other. The study of the stability of such systems requires one to draw upon several branches of mathematics but most notably functional analysis. Feedback Systems: Input-Output Properties includes the most basic concepts of matrices and norms, the important fundamental theorems in input-output stability, and the requisite background material in advanced topics such as the small gain theorem and the passivity theorem. Audience: The text is appropriate for advanced graduate students and researchers in control theory, dynamical systems, and ordinary and partial differential equations. Contents: Preface to the Classics Edition; Preface; Acknowledgments; Note to the Reader; List of Symbols; Chapter I: Memoryless Nonlinearities; Chapter II: Norms; Chapter III: General Theorems; Chapter IV: Linear Systems; Chapter V: Applications of the Small Gain Theorem; Chapter VI: Passivity; Appendix A: Integrals and Series; Appendix B: Fourier Transforms; Appendix C: Convolution; Appendix D: Algebras; Appendix E: Bellman--Gronwall Lemma; References; Index Feedback Systems: Input-output Properties deals with the basic input-output properties of feedback systems. Emphasis is placed on multiinput-multioutput feedback systems made of distributed subsystems, particularly continuous-time systems. Topics range from memoryless nonlinearities to linear systems, the small gain theorem, and passivity. Norms and general theorems are also considered. This book is comprised of six chapters and begins with an overview of a few simple facts about feedback systems and simple examples of nonlinear systems that illustrate the important distinction between the questions of existence, uniqueness, continuous dependence, and boundedness with respect to bounded input and output. The next chapter describes a number of useful properties of norms and induced norms and of normed spaces. Several theorems are then presented, along with the main results concerning linear systems. These results are used to illustrate the applications of the small gain theorem to different classes of systems. The final chapter outlines the framework necessary to discuss passivity and demonstrate the applications of the passivity theorem. This monograph will be a useful resource for mathematically inclined engineers interested in feedback systems, as well as undergraduate engineering students. This book was the first and remains the only book to give a comprehensive treatment of the behavior of linear or nonlinear systems when they are connected in a closed-loop fashion, with the output of one system forming the input of the other. The study of the stability of such systems requires one to draw upon several branches of mathematics but most notably functional analysis. __Feedback Systems: Input-Output Properties__ includes the most basic concepts of matrices and norms, the important fundamental theorems in input-output stability, and the requisite background material in advanced topics such as the small gain theorem and the passivity theorem. **Audience:** The text is appropriate for advanced graduate students and researchers in control theory, dynamical systems, and ordinary and partial differential equations. **Contents:** Preface to the Classics Edition; Preface; Acknowledgments; Note to the Reader; List of Symbols; Chapter I: Memoryless Nonlinearities; Chapter II: Norms; Chapter III: General Theorems; Chapter IV: Linear Systems; Chapter V: Applications of the Small Gain Theorem; Chapter VI: Passivity; Appendix A: Integrals and Series; Appendix B: Fourier Transforms; Appendix C: Convolution; Appendix D: Algebras; Appendix E: Bellman--Gronwall Lemma; References; Index Content: Inside Front Cover , Page ii Front Matter , Page iii Copyright , Page iv PREFACE , Pages ix-x ACKNOWLEDGMENTS , Pages xi-xii NOTE TO THE READER , Page xiii LIST OF SYMBOLS , Pages xv-xvi I - MEMORYLESS NONLINEARITIES , Pages 1-9 , C.A. DESOER, M. VIDYASAGAR II - NORMS , Pages 10-35 , C.A. DESOER, M. VIDYASAGAR III - GENERAL THEOREMS , Pages 36-55 , C.A. DESOER, M. VIDYASAGAR IV - LINEAR SYSTEMS , Pages 56-135 , C.A. DESOER, M. VIDYASAGAR V - APPLICATIONS OF THE SMALL GAIN THEOREM , Pages 136-167 , C.A. DESOER, M. VIDYASAGAR VI - PASSIVITY , Pages 168-227 , C.A. DESOER, M. VIDYASAGAR A - INTEGRALS AND SERIES , Pages 229-234 B - FOURIER TRANSFORMS , Pages 235-237 C - CONVOLUTION , Pages 238-244 D - ALGEBRAS , Pages 245-251 E - BELLMAN-GRONWALL LEMMA , Pages 252-254 REFERENCES , Pages 255-260 INDEX , Pages 261-264 ELECTRICAL SCIENCE: A Series of Monographs and Texts , Pages ibc1-ibc2