Stability analysis of a class of switched nonlinear systems using the time scale theory. (August 2019)

• Record Type: Journal Article
• Authors: Taousser, Fatima Z.; Defoort, Michael; Djemai, Mohamed; Djouadi, Seddik M.; Tomsovic, Kevin
• Is Part Of: Nonlinear analysis. Volume 33(2019)
• Page Start: 195
• Page End: 210
• Publication Date: 2019-08
• Subjects: Time scales -- Switched systems -- Stability analysis -- Multi-agent systems -- Consensus; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2019.02.006
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: This paper investigates stability for a class of switched nonlinear systems evolving on a non-uniform time domain. The studied class of systems switch between a nonlinear continuous-time and a nonlinear discrete-time subsystem. This problem is formulated using time scale theory where the latter is formed by a union of disjoint intervals with variable lengths and variable gaps. Using Gronwall's inequality and properties of the time scale exponential function, sufficient conditions are derived to ensure exponential stability. The results can be applied to cases where the continuous-time subsystem or the discrete-time subsystem is not necessarily stable, and the state matrices of each subsystem are not necessarily pairwise commuting. To illustrate the effectiveness of the proposed scheme, the consensus problem for general linear multi-agent systems under intermittent information transmissions is studied under this framework.