Construction of global Lyapunov functions using radial basis functions

✍ Scribed by Peter Giesl (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2007
• Tongue: English
• Leaves: 180
• Series: Lecture Notes in Mathematics 1904
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages I-VIII
Introduction....Pages 1-10
Lyapunov Functions....Pages 11-59
Radial Basis Functions....Pages 61-98
Construction of Lyapunov Functions....Pages 99-114
Global Determination of the Basin of Attraction....Pages 115-132
Application of the Method: Examples....Pages 133-147
Back Matter....Pages 149-170

✦ Subjects

Dynamical Systems and Ergodic Theory; Approximations and Expansions; Ordinary Differential Equations