Liapunov Functions and Stability in Control Theory

ISBN-13: 9783642059681 / Angielski / Miękka / 2010 / 237 str.

Andrea Bacciotti; Lionel Rosier

Opis

This book presents a modern and self-contained treatment of the Liapunov method for stability analysis, in the framework of mathematical nonlinear control theory. A Particular focus is on the problem of the existence of Liapunov functions (converse Liapunov theorems) and their regularity, whose interest is especially motivated by applications to automatic control. Many recent results in this area have been collected and presented in a systematic way. Some of them are given in extended, unified versions and with new, simpler proofs. In the 2^nd edition of this successful book several new sections were added and old sections have been improved, e.g., about the Zubovs method, Liapunov functions for discontinuous systems and cascaded systems. Many new examples, explanations and figures were added making this book accessible and well readable for engineers as well as mathematicians.

Recenzje

Review in amazon:

Super Book December 16, 2002 P, Princeton:
Bacciotti and Rosier have managed to present a nonformal, yet rigorous and well-organized introduction to nonlinear stabilization and controllability. They have definetly captured the most important research trends in the area and have managed to cover a wide range of topics with appropriate deepness. My only suggestion would be to add a list of symbols to the book and to discuss Chow's Theorem and the accessibility rank condition. Thanks for a great book!

From the reviews of the second edition:

"This book has been written by famous scientists in the areas of stability and control theories. It presents a modern and self-contained treatment of the Lyapunov method for stability analysis in the framework of mathematical nonlinear control theory. ... In the 2nd edition of this successful book several new sections have been added and old sections have been improved. A lot of new examples, explanations and figures are added making this book accessible and well readable for engineers as well as mathematicians." (Alexander O. Ignatyev, Zentralblatt MATH, Vol. 1078, 2006)

Spis treści

Differential equations.- Time invariant systems.- Time varying systems.- Differential inclusions.- Additional properties of strict Liapunov functions.- Monotonicity and generalized derivatives.