Necessary and sufficient conditions for leader-following consensus of multi-agent systems with random switching topologies

Abstract

This paper is concerned with leader-following consensus of general linear multi-agent systems with random switching topologies, where the dwell time in each topology consists of a fixed part and random part, and the topology switching signal in random part is modeled by a semi-markov process. First, a semi-Markov switched system with state jumps is constructed, and the stochastic stability of the constructed system is shown to be equivalent to that of the original system. Then a necessary and sufficient condition is established by using a Lyapunov approach in terms of linear matrix inequalities. Finally, the effectiveness of our results is illustrated by a numerical example and a practical example.