Construction of Global Lyapunov Functions Using Radial Basis Functions

by Peter Giesl

Overview

The basin of attraction of an equilibrium of an ordinary differential equation can be determined using a Lyapunov function. A new method to construct such a Lyapunov function using radial basis functions is presented in this volume intended for researchers and advanced students from both dynamical systems and radial basis functions. Besides an introduction to both areas and a detailed description of the method, it contains error estimates and many examples.

Product Details

ISBN-13:	9783540699071
Publisher:	Springer Berlin Heidelberg
Publication date:	05/18/2007
Series:	Lecture Notes in Mathematics , #1904
Edition description:	2007
Pages:	171
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

Lyapunov Functions.- Radial Basis Functions.- Construction of Lyapunov Functions.- Global Determination of the Basin of Attraction.- Application of the Method: Examples.

Editorial Reviews

From the reviews:

"In this book the author presents a new method to construct such a Lyapunov function using radial basis functions. Besides an introduction to both areas and a detailed description of the method, it contains error estimates and a lot of examples. This book is intended for researchers and advanced students from both dynamical systems and radial basis functions." (Alexander O. Ignatyev, Zentralblatt MATH, Vol. 1121 (23), 2007)

"In the monograph under review a method for the numerical computation of Lyapunov functions is developed. … one cannot only learn about how to compute Lyapunov functions, but can in fact learn a lot about their theoretical properties and about approximation methods using radial basis functions. … In summary, the book can be strongly recommended to anyone interested in either Lyapunov functions or in approximation methods using radial basis functions … . it is also very suitable for self study." (Lars Grüne, Mathematical Reviews, Issue 2009 i)

From the Publisher