Robust distributed consensus tracking for stochastic linear multi-agent systems under directed switching topologies

This paper investigates a robust mean-square exponential consensus tracking problem for a class of Itô stochastic linear multi-agent systems in the presence of stochastic noises and directed switching topologies. The desired tracking trajectory is only available to a small group of followers. By only using the relative state information among the neighbors and themselves, a distributed consensus tracking protocol is designed to achieve robust consensus tracking. A multi-step design procedure is developed for designing the feedback controller gain matrix in the protocol. Based on an average dwell time (ADT) approach, sufficient conditions on robust mean-square exponential consensus tracking are derived via the tools from M-matrix theory, graph theory, Lyapunov function analysis, and Itô stochastic theory. Numerical simulation is provided to illustrate the effectiveness of the theoretical result.