Nonlinear systems analysis

M. Vidyasagar9780898715262, 0898715261

When M. Vidyasagar wrote the first edition of Nonlinear Systems Analysis, most control theorists considered the subject of nonlinear systems a mystery. Since then, advances in the application of differential geometric methods to nonlinear analysis have matured to a stage where every control theorist needs to possess knowledge of the basic techniques because virtually all physical systems are nonlinear in nature.
The second edition, now republished in SIAM’s Classics in Applied Mathematics series, provides a rigorous mathematical analysis of the behavior of nonlinear control systems under a variety of situations. It develops nonlinear generalizations of a large number of techniques and methods widely used in linear control theory. The book contains three extensive chapters devoted to the key topics of Lyapunov stability, input-output stability, and the treatment of differential geometric control theory. In addition, it includes valuable reference material in these chapters that is unavailable elsewhere. The text also features a large number of problems that allow readers to test their understanding of the subject matter and self-contained sections and chapters that allow readers to focus easily on a particular topic.

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Table of contents :
Nonlinear Systems Analyhsis, Second Edition……Page 1
CONTENTS……Page 12
PREFACE TO THE CLASSICS EDITION……Page 14
PREFACE……Page 16
NOTE TO THE READER……Page 18
1. INTRODUCTION……Page 20
2. NONLINEAR DIFFERENTIAL EQUATIONS……Page 25
3. SECOND-ORDER SYSTEMS……Page 72
4. APPROXIMATE ANALYSIS METHODS……Page 107
5. LYAPUNOV STABILITY……Page 154
6. INPUT-OUTPUT STABILITY……Page 289
7. DIFFERENTIAL GEOMETRIC METHODS……Page 395
A. PREVALENCE OF DIFFERENTIAL EQUATIONS WITH UNIQUE SOLUTIONS……Page 488
B. PROOF OF THE KALMANYACUBOVITCH LEMMA……Page 493
C. PROOF OF THE FROBENIUS THEOREM……Page 498
References……Page 505
INDEX……Page 512