Construction method of Lyapunov functions based on eigen analysis

Author

Nishimura, Yuki ; Yamashita, Yuh ; Tanaka, Kanya ; Wakasa, Yuji

Author_Institution

Grad. Sch. of Sci. & Eng., Yamaguchi Univ., Ube, Japan

fYear

2009

fDate

18-21 Aug. 2009

Firstpage

691

Lastpage

694

Abstract

In this paper, we show discretized Lyapunov functions for various nonlinear dynamical systems by using the method that the authors have proposed. We use Kushner´s scheme of difference approximation with directions and Alcaraz et al.´s quantization of Markov processes to approximate Lyapunov equations by linear Schroumldinger-like equations. We construct time-invariant functions concerned with the solutions to Schroumldinger-like equations. Then, we show the effectiveness of the method via an example.

Keywords

Lyapunov matrix equations; Markov processes; Schrodinger equation; approximation theory; difference equations; nonlinear equations; Kushners scheme; Markov process; construction method; difference approximation; discretized Lyapunov function; eigen analysis; linear Schroumldinger-like equation; matrix theory; nonlinear dynamical system; time-invariant function; Difference equations; Differential equations; Eigenvalues and eigenfunctions; Information analysis; Information science; Lyapunov method; Markov processes; Nonlinear equations; Quantization; Stochastic processes; Lyapunov theory; Nonlinear systems; Schrödinger-like equation; difference approximation; eigenvalue analysis;

fLanguage

English

Publisher

ieee

Conference_Titel

ICCAS-SICE, 2009

Conference_Location

Fukuoka

Print_ISBN

978-4-907764-34-0

Electronic_ISBN

978-4-907764-33-3

Type

conf

Filename

5334292