2002 / xviii + 498 pages / Softcover / ISBN: 978-0-898715-26-2 / List Price $74.50 / SIAM Member Price $52.15 / Order Code CL42
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.
This text is designed for use at the graduate level in the area of nonlinear systems and as a resource for professional researchers. The subject of nonlinear systems continues to interest not only theorists but also practitioners working in areas such as robotics, spacecraft control, motor control, and power systems. This book is sure to enlighten readers on this timeless and ever-fascinating subject.
Preface to the Classics Edition; Preface; Note to the Reader; Chapter 1: Introduction; Chapter 2: Nonlinear Differential Equations; Chapter 3: Second-Order Systems; Chapter 4: Approximate Analysis Methods; Chapter 5: Lyapunov Stability; Chapter 6: Input-Output Stability; Chapter 7: Differential Geometric Methods; Appendix A: Prevalence of Differential Equations with Unique Solutions; Appendix B: Proof of the Kalman-Yacubovitch Lemma; Appendix C: Proof of the Frobenius Theorem; References; Index.
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