A Sufficient Condition for the Stability of Discrete-Time Systems With State-Dependent Coefficient Matrices

Author

Yuno, Tsuyoshi ; Ohtsuka, Toshiyuki

Author_Institution

Dept. of Syst. Innovation, Osaka Univ., Toyonaka, Japan

Volume

59

Issue

1

fYear

2014

fDate

Jan. 2014

Firstpage

243

Lastpage

248

Abstract

There is no systematic method of checking the stability of general nonlinear systems. In this study, we focus on discrete-time autonomous systems with state-dependent coefficient matrices. Sufficient conditions for local and global asymptotic stabilities are given for upper-triangularizable systems. The transformation matrix for triangularization is not required explicitly for checking such conditions. Moreover, the system may have nondifferentiability at the origin, which is an advantage of our approach over Lyapunov´s indirect method.

Keywords

Lyapunov methods; asymptotic stability; discrete time systems; matrix algebra; nonlinear control systems; Lyapunov indirect method; discrete-time autonomous systems; discrete-time systems stability; general nonlinear systems; global asymptotic stabilities; local asymptotic stabilities; nondifferentiability; state-dependent coefficient matrices; upper-triangularizable systems; Algebraic methods; Lie algebra; asymptotic stability; discrete-time systems; nonlinear systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2013.2270318

Filename

6544591