Title :
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
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;
Conference_Titel :
ICCAS-SICE, 2009
Conference_Location :
Fukuoka
Print_ISBN :
978-4-907764-34-0
Electronic_ISBN :
978-4-907764-33-3
