Nonlinear Systems Analysis (Classics in Applied Mathematics) 2nd Edition by M. Vidyasagar (PDF)

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When the first edition of this book was published, 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. 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. The text also features a large number of problems that allow readers to test their understanding, and self-contained sections and chapters that make particular topics more accessible.

User’s Reviews

Editorial Reviews: Book Description This text provides a rigorous mathematical analysis of the behavior of nonlinear control systems under a variety of situations. Book Description This second edition text provides a rigorous mathematical analysis of the behavior of nonlinear control systems under a variety of situations. Three chapters cover the topics of Lyapunov stability, input-output stability, and the treatment of differential geometric control theory, with reference material unavailable elsewhere. About the Author 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. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book by Vidyasagar is a classic. However, I feel that Khalil is a more reader-friendly book, if you are taking a course. The best thing I liked about the book is that results are not merely stated, but the author has tried to provide an intuition or a physical interpretation of the result.The flip side is that examples and exercise problems are too few in number, but I think that this will be a very good book to learn from if the course is taught by a very good instructor.

⭐Well written and easy to read for the non-specialist. A great introduction to the fundamentals of nonlinear systems.

⭐Vid. is an excellent expositor. The material is presented rigourously, which might be standard for texts dealing with this subject, but also economically, which is not typical (read: Khalil). The most important distinction of this book however is that the author consistently explains the intuitions and motivation behind the theory (one example of many: what does a matrix norm mean “physically?”). This instead of you wading through mounds of mathematics never knowing why. The author is himself a practicing engineer, not an ivory tower researcher and this fortunate bias is evidenced in this book.This text is unique in that it introduces the matrix measure (available elsewhere only in journal papers), a very useful technique that I personally have used in my own research. The final chapter on geometric methods distilled the essence of the very deep and daunting book by Van der Shaft, from which my course instructor culled his lecture notes. I was ahead of the curve in understanding the material thanks to this book.In short, as an expositor nobody beat Vidyasagar.Problems: I have the newly republished SIAM edition, ostensibly a photocopy of the ’92 printing. Therefore the print is at times ever-so-slightly blurred, and an upside down figure from the ’92 printing has not been corrected (p. 457).

⭐This is an elegant treatment of nonlinear systems concentrating on stability and controls. It includes all of the material in the textbooks only without the verbage. The treatment is deep and outstanding and parallels that of Khalil’s and Isidori’s books. The only caveat is that the book does assume a pretty good mathematical background from the reader and some experience reading very advanced mathematical tomes – some of the notation is never defined but those having the presumed background will not find this a problem. For the advanced student/practitioner.

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