Formation Static Output Control of Linear Multi-Agent Systems With Hidden Markov Switching Network Topologies

Abstract

This paper addresses the $\mathcal {H}_{2}$ , $\mathcal {H}_\infty $ and mixed $\mathcal {H}_{2}/\mathcal {H}_\infty $ formation static output control of continuous-time linear multi-agent systems with Markovian switching network topologies. It is assumed that the operation mode of the network topology cannot be directly measured but, instead, can be estimated by an imperfect detector. To model this problem, we consider a continuous-time hidden Markov model, in which the hidden component represents the real operation mode of the network topology while the observed component represents the information emitted from the detector and available for the controller. It is also assumed that only a partial information from the state variables of the multi-agent systems is available. By using an LMI (linear matrix inequality) formulation, a distributed static output controller which switches according to the detector information is designed to guarantee the stability in the mean square sense of the closed loop system, as well as an upper-bound for an index performance. Three situations are considered for the performance criteria: the $\mathcal {H}_{2}$ norm, the $\mathcal {H}_\infty $ norm, and the mixed $\mathcal {H}_{2}/\mathcal {H}_\infty $ norms. The paper is concluded with a numerical example to illustrate the effectiveness of the theoretical results.