Constructions of Strict Lyapunov Functions / Edition 1

by Michael Malisoff, Frïdïric Mazenc

Overview

Converse Lyapunov function theory guarantees the existence of strict Lyapunov functions in many situations, but the functions it provides are often abstract and nonexplicit, and therefore may not lend themselves to engineering applications. Often, even when a system is known to be stable, one still needs explicit Lyapunov functions; however, once an appropriate strict Lyapunov function has been constructed, many robustness and stabilization problems can be solved through standard feedback designs or robustness arguments. Non-strict Lyapunov functions are often readily constructed.

This book contains a broad repertoire of Lyapunov constructions for nonlinear systems, focusing on methods for transforming non-strict Lyapunov functions into strict ones. Their explicitness and simplicity make them suitable for feedback design, and for quantifying the effects of uncertainty. Readers will benefit from the authors’ mathematical rigor and unifying, design-oriented approach, as well as the numerous worked examples.

Product Details

ISBN-13:	9781848825345
Publisher:	Springer London
Publication date:	06/29/2009
Series:	Communications and Control Engineering
Edition description:	2009
Pages:	386
Product dimensions:	6.40(w) x 9.30(h) x 1.10(d)

Table of Contents

Background.- Background on Nonlinear Systems.- Review of Lyapunov Functions.- Time-Invariant Case.- Matrosov Conditions: Simple Case.- Jurdjevic-Quinn Conditions.- Systems Satisfying the Conditions of LaSalle.- Time-Varying Case.- Strictification: Basic Results.- Backstepping for Time-Varying Systems.- Matrosov Conditions: General Case.- Adaptively Controlled Systems.- Systems with Multiple Time Scales.- Rapidly Time-Varying Systems.- Slowly Time-Varying Systems.- Hybrid Time-Varying Systems.

Editorial Reviews

From the reviews:

“This monograph covers a wide range of nonlinear dynamical systems, including Jurdjevic-Quinn systems, time-varying systems satisfying LaSalle or Matrosov conditions, adaptively controlled dynamics, slowly and rapidly time-varying systems, and hybrid time-varying systems. … The book will be useful to researchers and graduate students in various areas of applied mathematics and control theory and engineering.” (Vladimir Sobolev, Zentralblatt MATH, Vol. 1186, 2010)

“This is an important and painstaking chore. … The book is a combination of a research monograph and an expository text. … those who need to analyze or to perform a detailed stability or stabilization analysis of concrete equations will find the book a very good source of ideas and references. … should be a desired addition to all libraries that serve mathematics departments and control engineering faculties. … could be used successfully as reading material for advanced graduate students interested in the subject matter.” (Zvi Artstein, SIAM Review, Vol. 53 (1), 2011)

From the Publisher