H ∞ consensus of multi-agent systems with semi-Markovian switching topologies and mode-dependent delays

Abstract

This paper addresses leader-following consensus of multi-agent systems with semi-Markovian switching topologies and time-varying delays. Unlike the classic Markovian switching topologies, the transition rates are time-varying in the semi-Markovian switching topologies, which can better model the switching of topologies due to inevitable stochastic changes. Moreover, compared with existing works on multi-agent systems with switching topologies and time delays, the delays in the paper are dependent on the switching modes. By designing the distributed mode-dependent consensus protocol and constructing Lyapunov functional, sufficient conditions in terms of LMIs are derived to ensure that leader-following consensus is asymptotically achieved in the mean square. Finally, a numerical example is provided to show the effectiveness of the main results.