Consensus tracking for general linear stochastic multi-agent systems: a sliding mode variable structure approach

This study deals with the consensus tracking problem for general linear multi-agent systems driven by Brownian motion. A directed graph is used to represent the communication topology of the multi-agent network. To solve the consensus tracking problem, an innovative concept of the sub-reachability of the sliding motion to approach approximately the specified sliding surface is introduced. Under the concept of sub-reachability, the sliding mode variable structure consensus tracking protocol is synthesised to guarantee the sub-reachability of the sliding motion in a finite time. By using the auxiliary function method and stochastic It (O) over cap integrals techniques with respect to Brownian motion, a sufficient condition for mean square asymptotic consensus tracking is derived. In particular, the consensus tracking criteria are very concise and can be implemented easily. Finally, a simulation example is utilised to illustrate the usefulness of the proposed control protocol.