Adaptive distributed tracking control for Markov jump multiagent systems with a non-strict leader

This paper investigates the leader-following mean square distributed tracking control problem (DTCP) for a Markov jump multiagent systems (MJMASs) with the general linear dynamical model over an undirected graph. The non-strict control input of the leader is non-zero, unknown, and unavailable to any followers. First, the jump characteristics of the system for the single agent is modeled by a continuous Markov chain. Second, in order to address the leader–follower mean square DTCP, the distributed mode-dependent static controller and the fully distributed mode-dependent adaptive controller are designed for all followers based on the information from the agents’ neighbors and itself, respectively. Then, to further analyze the stability of the MJMASs, two categories of decomposed related Lyapunov functions are constructed using Lyapunov stability theory. The sufficient conditions for the existence of the distributed controller are obtained by derivation. Finally, two simulation cases are presented to verify the validity and feasibility of the proposed strategies.