On Estimation of Reachable Sets for Approximate Consensus of Homogeneous Multiagent Systems Subject to Bounded Exogenous Disturbances

Abstract

This paper is concerned with the reachable set estimation for leaderless discrete-time homogeneous multiagent systems (MASs) with general linear high-order dynamics and bounded exogenous disturbances. The interagent interactions are described by undirected connected graphs, where fixed and randomly switching manners are considered. To govern the evolution of the randomly switching, a Markov chain is introduced with consideration of completely and partially known transition probabilities. By collecting in-neighbors' information, the protocol is designed to ensure certain properties, including (I) the state trajectories of all agents are constrained within a compact set; (II) the noise-unperturbed MAS achieves asymptotic consensus in the exponential stability sense; (III) the approximate consistency is regulated for the noise-perturbed MAS in the input-to-state stability sense. Thanks to the constructed nonsingular transformation, one explicitly characterizes the agreement dynamics by the consensus function with determined initial condition. It is deduced that the intersection of estimated reachable sets of the concerned MAS and the agreement dynamics is nonempty. Numerical simulations confirm the theoretical analysis.