Reachable set synthesis of nonlinear heterogeneous multi-agent systems with Markov switching topologies

This study addresses the problem of reachable set synthesis for nonlinear leaderless heterogeneous multi-agent systems (NLHMASs) under Markov switching topologies. Currently, there exists a paucity of relevant studies on NLHMASs under Markov switching topologies. However, the communication topologies of NLHMASs plays a crucial role in their collaboration, and Markov switching topologies capture the randomness of communication more effectively than fixed topologies. Motivated by this gap, the NLHMASs under Markov switching topologies are considered in this paper, and a consensus protocol in the form of proportional derivative state feedback is designed. Then, by applying Lyapunov functional theory, sufficient conditions described in the form of linear matrix inequalities (LMIs) are derived to guarantee that the reachable set of the systems is bounded by a compact ellipsoid. To increase the feasibility of solutions for LMIs in the sufficient conditions, the free-weighting matrix method is used. However, the introduction of the free-weighting matrix leads to a problem of matrix coupling. To solve this problem effectively, the gains are obtained by using the matrix transformation technique. The validity of the theoretical results is finally verified by a numerical example and practical verification.