Consensus of Multi‐Agent Systems with Switching Disconnected Topologies via Elementary‐Unit‐Based Dwell Time Approach

Abstract

In this study, a leader‐following consensus problem is investigated for a class of multi‐agent systems with switching disconnected topologies. Different from the existing results on switching disconnected topologies, the multi‐agent systems considered in this study are unstable. In this situation, the disconnected agents can disperse over some periods even if there exists control protocol on them. To break through this challenge, we draw lessons from which an appropriate switching law can stabilize the switching unstable systems and propose a novel approach called elementary‐unit‐based dwell time (EUBDT) approach. Based on this approach, each switching interval is considered to consist of a certain number of elementary time segments. Then, by analyzing the local variation of the error states within each elementary time segment, the stabilization properties of switching behaviors are derived to compensate the divergence within the switching intervals. Based on this, the sufficient conditions for the leader‐following consensus can be obtained by using a novel kind of piecewise time‐varying Lyapunov functions (PTVLFs). Moreover, a time‐scheduled controller is designed for such system. Finally, a numerical simulation is given to illustrate the theoretical approach.