Improved delay-dependent consensus stability criteria of high-order multi-agent systems with time delays

Abstract

This paper studies the consensus of high-order multi-agent systems with communication time delays. In order to get the maximum allowable delay bound, an approach of system transformations is introduced. Through transformation the consensus problem is converted to the robust stability problem of some uncertain state-delayed system. The proposed method employs an improved vector Wirtinger-type inequality for constructing a novel Lyapunov–Krasovskii functional. Based on the Lyapunov stable theory, new sufficient conditions in terms of linear matrix inequalities which contain the feedback gain condition and delay condition are given to guarantee the average consensus under fixed topology and switching connected topologies, respectively. Maximum allowable delay bounds are further obtained for both systems. As long as the delays are less than this bound, there exist linear feedback consensus protocols driving the multi-agent system to achieve consensus. The effectiveness of the proposed method is demonstrated by numerical examples.