Liapunov Functions and Stability in Control Theory

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.

1st edition in LNCIS sold out in 18 months 2nd edition comes with many new examples, explanations and figures making it much better readable for engineers as well as mathematicians 3 new or improved chapters Includes supplementary material: sn.pub/extras

Autorentext

Andrea Bacciotti is full professor of Mathematical Analysis at Politecnico di Torino, Italy, where he also served as dean of the Mathematics Department. His research interests focus on ordinary differential equations, differential inclusions, mathematical control theory and switched systems theory. With Springer he already published the book Liapunov Functions and Stability in Control Theory (ISBN 978-3-540-21332-1).

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