Mean square consensus of double-integrator multi-agent systems under intermittent control: A stochastic time scale approach

Abstract

We consider the leader–follower consensus problem for a multi-agent system where information is exchanged only on a non-uniform discrete stochastic time domain. For a second-order multi-agent system subject to intermittent information exchange, we model the tracking error dynamics as a μ−varying linear system on a discrete stochastic time scale, where μ is the graininess operator. Based on a Lyapunov operator and a positive perturbation operator on the space of symmetric matrices, we derive necessary and sufficient conditions to design a decentralized consensus protocol. This protocol allows us to cast the mean-square exponential consensus problem within the framework of dynamic equations on stochastic time scales. We establish some theoretical results which allow for the computation of the control gain matrix which guarantees the mean-square exponential stability with a given decay rate for the error dynamics. To show the effectiveness of the theoretical results, some simulation and experimental results on multi-robot systems have been performed.