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Under a nonhomogeneous Markovian jump network topology, this paper addresses the problem of leader-following consensus for multi-agent systems with an asynchronous control mode. Specifically, based on an asynchronous mode-dependent Lyapunov function and a suitable relaxation process, sufficient conditions for leader-following consensus are derived in such a way that 1) non-convex terms multiplied by time-varying signed parameters can be addressed, 2) the emergence of an asynchronous control mode can be reflected in the control synthesis of the follower agents, and 3) the constraints of two combined parameters can be explicitly imposed on the process of transforming parameterized linear matrix inequalities (PLMIs) into LMIs. Finally, two illustrative examples are given to show the validity of the proposed method.

Leader-Following Consensus for Multi-Agent Systems With Asynchronous Control Modes Under Nonhomogeneous Markovian Jump Network Topology