Periodic event‐triggered consensus control for multi‐agent systems with switching jointly connected topologies

Abstract

The consensus problem for a class of multi‐agent systems with switching jointly connected topologies via periodic event‐triggered control is studied. The distinguishing feature of such system is that the eigenvalues of system matrix can contain positive real parts. Due to the coexistence of unstable system matrix and disconnected topologies, the agents can diverge from each other across some periods even if the control input is imposed on them. To overcome this difficulty, a periodic‐sampling time unit (PSTU) approach is introduced to analyse the local convergence or divergence property within each sampling time unit based on the periodic event‐triggering control. Then the stabilisation property of switching behaviours is utilised to compensate the divergence within each switching interval via the dwell time technique. It is interesting to see that each switching period is considered to consist of finite number of PSTUs. Then by confining a pair of lower and upper bounds on the dwell time, the overall consensus can be reached. Further, a novel class of event‐dependent discretised Lyapunov functions are utilised to describe the error characteristics and computable conditions for the overall consensus can be derived. Finally, the effectiveness of the proposed result is illustrated by a numerical example.