Liapunov Functions and Stability in Control Theory [electronic resource] / by Andrea Bacciotti, Lionel Rosier.Material type: TextLanguage: English Series: Communications and Control Engineering: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005Edition: 2nd EditionDescription: XIII, 237 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540273974Subject(s): Engineering | Systems theory | Physics | Vibration | Engineering | Control Engineering | Systems Theory, Control | Complexity | Vibration, Dynamical Systems, ControlAdditional physical formats: Printed edition:: No titleOnline resources: Click here to access online
Differential equations -- Time invariant systems -- Time varying systems -- Differential inclusions -- Additional properties of strict Liapunov functions -- Monotonicity and generalized derivatives.
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 2nd 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.