Fixed-time stability of switched systems with application to a problem of formation control. (May 2021) - Aleksandrov, A.Yu.; Andriyanova, N.R.
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.