Customer Reviews

Nonlinear Systems Analysis (Classics in Applied Mathematics) (No. 42)

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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).

Reviewer: NextNoName : )

The major portion of this book is on the conditions for stability of general nonlinear systems. The treatment is thorough. Stability is examined from both Lyapunov and I/O perspectives. Secondary portions are on quasi-linear approximation and differential geometry.

The commentaries of Dr. Vidyasagar at the beginning and end of each chapter are useful. This is because this book was written relatively recently by a master of this subject.

The thoughts flow well. I like the fact that the chapters are kept to only seven.

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.

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