Exponential consensus of second-order multi-agent systems with time-varying delay under switching network

This paper addresses exponential consensus problem of second-order multi-agent systems (MASs) with both time-varying communication delay and switching directed topology. A distinct feature of this MAS is that the interaction topology is switching orchestrated by an average dwell time (ADT) switching signal. Interestingly, the MAS can exhibit diverse consensus behavior including static consensus and dynamic consensus. By introducing a state transformation for the position and velocity simultaneously, the consensus problem is converted to the exponential stability problem of a reduced-order switched system. Then, by constructing piecewise Lyapunov-Krasovskii functionals, some sufficient conditions in form of linear matrix inequality for exponential consensus with a prescribed decay rate are derived. The lower bound of ADT for admissible switching signals is also calculated explicitly. Finally, numerical examples are presented to verify the theoretical results.