Double-integrator control for MASs with small switching dwell time

Distributed consensus tracking under variable communication network is an important research topic of multi-agent systems (MASs). Many results have been obtained for consensus of MASs with switching networks that are either jointly connected or periodically connected, but it remains challenging when the disconnected switching topologies are activated more frequently than the connected ones. This paper investigates both the consensus tracking and average consensus tracking problems for double-integrator MASs under switching topologies. By using the tools of multiple Lyapunov function and linear matrix inequality method, a neighbor-based distributed controller is designed for each following-agent so as to achieve (average) consensus tracking, even if the underlying switching communication network contains disconnected digraphs. Sufficient conditions, in terms of dwell time, total running time ratio of connected to disconnected topologies, and the exponentially convergent margin, are derived. Compared with existing research, the proposed method presents a quantified switching stability result allowing more disconnected digraphs to participate in switching, which can significantly reduce the communication pressure in applications. Simulation results are finally provided to verify the theoretical analysis.