On robust stability analysis of uncertain discrete-time switched nonlinear systems with time varying delays
type: Item
instance of: scholarly article
title: On robust stability analysis of uncertain discrete-time switched nonlinear systems with time varying delays
zbMATH Open document ID: 1427.93186
DOI: 10.1155/2018/6354979
author: Marwen Kermani
author: Anis Sakly
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: This paper provides new sufficient conditions on robust asymptotic stability for a class of uncertain discrete-time switched nonlinear systems with time varying delays. The main focus will be dedicated to development of new algebraic criteria to break with classical criteria in terms of linear matrix inequalities (LMIs). Firstly, by contracting a new common Lyapunov-Krasovskii functional as well as resorting to the M-matrix proprieties, a novel robust stability criterion under arbitrary switching signals is derived. Secondly, the obtained result is extended for a class of switched nonlinear systems modeled by a set of differences equations by applying the aggregation techniques, the norm vector notion, and the Borne-Gentina criterion. Furthermore, a generalization for switched nonlinear systems with multiple delays is proposed. The main contribution of this work is that the obtained stability conditions are algebraic and simple. In addition, they provide a solution of the most difficult problem in switched systems, which is stability under arbitrary switching, and enable avoiding searching a common Lyapunov function considered as a very difficult task even for some low-order linear switched systems. Finally, two examples are given, with numerical simulations, to show the merit and effectiveness of the proposed approach.
Mathematics Subject Classification ID: 93D09
Mathematics Subject Classification ID: 39A30
Mathematics Subject Classification ID: 93C30
Mathematics Subject Classification ID: 93D20
zbMATH DE Number: 7019282
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/6354979
OpenAlex ID: W2885157867
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Wikidata QID: Q129358769
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description: scientific article; zbMATH DE number 7019282