On reachable set estimation of multi-agent systems

In this paper, the problem of reachable set estimation of multi-agent systems (MASs) is investigated. For the ease of application, balanced communication topology with a directed spanning tree and non-zero initial condition are considered. Based on the Lyapunov method and orthogonal transformation technique, sufficient conditions are established in terms of linear matrix inequalities to guarantee that the reachable set of MASs is bounded by a compact ellipsoid. Moreover, by employing some useful skills from stochastic analysis, the result is then extended to the problem for MASs under Markovian switching topologies. The effectiveness of the obtained results is illustrated by two numerical examples.