Nonlinear Systems Analysis / Edition 2

Nonlinear Systems Analysis / Edition 2

by Vidyasagar
     
 

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… See more details below

Overview

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.


About the Authors

M. Vidyasagar is Executive Vice President of Tata Consultancy Services in Hyderabad, India. He has held numerous academic visiting positions with universities such as MIT, the University of California, and Tokyo Institute of Technology and has also held various consultancy positions within the field. In addition, he has published many articles in linear, nonlinear, and robust control theory; robotics; and statistical learning theory. He has authored or co-authored more than a half dozen books on these topics.

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Product Details

ISBN-13:
9780136234630
Publisher:
Prentice Hall Professional Technical Reference
Publication date:
07/28/1992
Edition description:
2nd ed
Pages:
498
Product dimensions:
7.01(w) x 9.25(h) x (d)

Table of Contents

Preface
Note to the Reader
1Introduction1
2Nonlinear Differential Equations6
2.1Mathematical Preliminaries6
2.2Induced Norms and Matrix Measures19
2.3Contraction Mapping Theorem27
2.4Nonlinear Differential Equations33
2.5Solution Estimates46
3Second-Order Systems53
3.1Preliminaries53
3.2Linearization Method57
3.3Periodic Solutions67
3.4Two Analytical Approximation Methods79
4Approximate Analysis Methods88
4.1Describing Functions88
4.2Periodic Solutions: Rigorous Arguments109
4.3Singular Perturbations127
5Lyapunov Stability135
5.1Stability Definitions135
5.2Some Preliminaries147
5.3Lyapunov's Linearization Method157
5.4Stability of Linear Systems193
5.5Lyapunov's Linearization Method209
5.6The Lur'e Problem219
5.7Converse Theorems235
5.8Applications of Converse Theorems246
5.9Discrete-Time Systems264
6Input-Output Stability270
6.1L [Subscript p] Spaces and their Extensions271
6.2Definitions of Input-Output Stability277
6.3Relationships Between I/O and Lyapunov Stability284
6.4Open-Loop Stability of Linear Systems292
6.5Linear Time-Invariant Feedback Systems309
6.6Time-Varying and/or Nonlinear Systems337
6.7Discrete-Time Systems365
7Differential Geometric Methods376
7.1Basics of Differential Geometry377
7.2Distributions, Frobenius Theorem392
7.3Reachability and Observability399
7.4Feedback Linearization: Single-Input Case427
7.5Feedback Linearization: Multi-Input Case438
7.6Input-Output Linearization456
7.7Stabilization of Linearizable Systems464
A. Prevalence of Differential Equations With Unique Solutions469
B. Proof of the Kalman-Yacubovitch Lemma474
C. Proof of the Frobenius Theorem476
References486
Index493

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