Time-Varying Formation Control of General Linear Multi-Agent Systems Under Markovian Switching Topologies and Communication Noises

This brief studies the time-varying formation (TVF) control of linear multi-agent systems (MASs), where the communication topology switches from several different topologies and the switching signal is depicted by a right-continuous Markov process. The communication noises are taken into account simultaneously, which are described as independent white noises with noisy intensities. A class of stochastic-approximation type control protocols is given and certain sufficient conditions are derived for realizing the TVF stabilization in mean square sense. Moreover, the indicative function and infinitesimal generator are imported in Lyapunov functions to help proving that the MASs can be formed into stable TVF shapes with the proposed control protocols. In the end, an simulation example is performed to state the availability of the approach.