Maximum allowable delay bound for consensus of general linear multi-agent systems

This paper studies the consensus of general linear multi-agent systems with uniform delay and focuses on searching a maximum allowable delay bound. Both fixed and switching topology cases are discussed. Through a series of system transformations the consensus problem is converted to the robust stability problem of some uncertain state-delayed system. By using Lyapunov-Krasovskii function analysis, consensus conditions which contain the feedback gain condition and delay condition are proposed for systems under fixed topology and switching connected topologies, respectively. Maximum allowable delay bounds are further obtained for both systems. As long as the delay is less than this bound, there exist linear feedback consensus protocols driving the multi-agent system to achieve consensus. Numerical examples are given to illustrate the results.