On consensus of high-order multi-agent systems with directed interactions and asymmetric communication delays

This paper focuses on the consensus problem for high-order multi-agent systems (MAS) with directed interactions and asymmetric time-varying communication delays. By introducing an orthogonal linear transformation, we prove that the consensus of such MAS is achieved if and only if each solution of an equivalent reduced-order system converges to zero. Based on this nature and Lyapunov-Krasovskii functional approach, we then establish several sufficient convergence conditions which are characterized by linear matrix inequalities. Furthermore, we give a Lyapunov-like design for the explicit selection of protocol parameters, which is robust to asymmetric time-varying delays and fixed or switching directed topologies. Also, we show that the solutions of these linear matrix inequalities always exist under the assumptions on network topology and protocol parameters. As application, we construct a state-feedback controller for the consensus of MAS with agent modeled by a completely controllable single-input linear time-invariant system.