A Relaxed Small-Gain Theorem for Interconnected Discrete-Time Systems

Author

Geiselhart, Roman ; Lazar, Mircea ; Wirth, Fabian R.

Author_Institution

Inst. for Math., Univ. of Wurzburg, Würzburg, Germany

Volume

60

Issue

3

fYear

2015

fDate

Mar-15

Firstpage

812

Lastpage

817

Abstract

This technical note presents a relaxation of the small-gain theorem for the stability analysis of interconnected discrete-time nonlinear systems. The distinctive feature of this relaxation is that separate systems may be unstable, while global asymptotic stability (GAS) of the overall interconnected systems equilibrium is obtained. In addition, a Lyapunov function for the overall interconnected system is explicitly derived. Necessity of the hypothesis of the small-gain theorem is established for a rather general class of GAS nonlinear systems. An illustrative example demonstrates the non-conservatism of the developed small-gain theorem.

Keywords

Lyapunov methods; asymptotic stability; discrete time systems; nonlinear control systems; GAS; Lyapunov function; distinctive feature; global asymptotic stability; interconnected discrete-time nonlinear systems; interconnected discrete-time systems; overall interconnected system; relaxed small gain theorem; small-gain theorem; stability analysis; Asymptotic stability; Discrete-time systems; Interconnected systems; Lyapunov methods; Nonlinear systems; Stability analysis; Vectors; Discrete-time nonlinear systems; Lyapunov methods; non-conservative small-gain theorems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2014.2332691

Filename

6843917