NONLINEAR SYSTEMS ANALYSIS VIDYASAGAR PDF

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. 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.

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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. 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.

Since that time, several developments have taken place in this area which have made it desirable to update the contents of the book. Accordingly, virtually the entire book has been rewritten. The most notable changes are the following: 1 During the past decade, there have been some significant advances in the area of nonlinear control system design based on the use of differential geometric methods.

Thus it is imperative that anyone interested in nonlinear system theory should have at least a passing acquaintance with these methods.

In this second edition, I have included a new chapter which discusses the differential geometric approach Chapter 7. Topics covered include reachability, observability, and feedback linearization in both the input-state and input-output settings , zero dynamics, and the stabilization of linearizable systems. In addition to presenting the theory, I have also included some applications of the theory to problems in robotics.

Motivated by this chapter, an interested and diligent student could pursue a more rigorous course of study with an advanced text. Some of these results are included in the present edition, such as: observer-controller stabilization of nonlinear systems, and the stability of hierarchical systems Section 5.

In addition to the above, Section 4. Two examples of such books are: Stability of Motion by W. Desoer and myself.

At the same time some of the techniques presented in these books are finding new and previously unsuspected applications. With this in mind, in the present edition I have included some relevant material from these and other classic books, such as the converse Lyapunov theory Section 5. Appendix A describes a sixty year-old theorem due to Witold Orlicz, on the prevalence of differential equations with unique solutions.

This paper is quite inaccessible, but its contents deserve wide dissemination. The contents of the last two appendices are of course readily available elsewhere, but their inclusion in the present text makes it more self-contained.

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Nonlinear systems analysis

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. The second edition provides a rigorous When the first edition of this book was published, most control theorists considered the subject of nonlinear systems a mystery. The second edition 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. It contains three extensive chapters devoted to the key topics of Lyapunov stability, input-output stability, and the treatment of differential geometric control theory. Moreover, valuable reference material included in these chapters is unavailable elsewhere.

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