Fixed-time stability of switched systems with application to a problem of formation control. (May 2021)

• Record Type: Journal Article
• Authors: Aleksandrov, A.Yu.; Andriyanova, N.R.
• Is Part Of: Nonlinear analysis. Volume 40(2021)
• Publication Date: 2021-05
• Subjects: Switched system -- Differential inequality -- Fixed-time stability -- Multiple Lyapunov function -- Multiagent system -- Equidistant deployment; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2020.101008
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: The problem of fixed-time stability of switched systems is studied. With the aid of the multiple Lyapunov function method, constraints on switching signals are derived under which global fixed-time stability of zero solutions of considered systems can be guaranteed. Sufficient conditions of fixed-time stability for Persidskii-type systems are obtained. The developed approaches are applied to the problem of the fixed-time deployment of mobile agents over a line segment under protocols with switched communication topology. Efficiency of the obtained results is demonstrated by a numerical simulation. Highlights: Using the multiple Lyapunov functions method, constraints on switching signals are derived under which global fixed-time stability for the corresponding switched systems can be guaranteed. Sufficient conditions of global fixed-time stability for Persidskii-type systems are obtained. An approach to design control protocols providing fixed-time deployment of mobile agents over a line segment under switching communication topology is proposed.