title: Perturbed dynamics of discrete-time switched nonlinear systems with delays and uncertainties.
abstract: This paper addresses the dynamics of a class of discrete-time switched nonlinear systems with time-varying delays and uncertainties and subject to perturbations. It is assumed that the nominal switched nonlinear system is robustly uniformly exponentially stable. It is revealed that there exists a maximal Lipschitz constant, if perturbation satisfies a Lipschitz condition with any Lipschitz constant less than the maximum, then the perturbed system can preserve the stability property of the nominal system. In situations where the perturbations are known, it is proved that there exists an upper bound of coefficient such that the perturbed system remains exponentially stable provided that the perturbation is scaled by any coefficient bounded by the upper bound. A numerical example is provided to illustrate the proposed theoretical results.
authors.affiliation: College of Electrical and Information Engineering, Southwest University for Nationalities of China, Chengdu, Sichuan 610041, China. Electronic address: xingwenliu@gmail.com.
authors.forename: Xingwen
authors.initials: X
authors.lastname: Liu
authors.affiliation: School of Science, Hubei University for Nationalities, Hubei 445000, China. Electronic address: jcheng6819@126.com.
authors.forename: Jun
authors.initials: J
authors.lastname: Cheng
keywords: Delays; Nonlinear systems; Perturbations; Stability; Switched systems; Uncertainties