Distributed consensus protocol for leader-following multi-agent systems with functional observers

This paper considers the consensus problem of the leader-following multi-agent systems under directed interaction topology. The dynamics of each agent is modeled by a general form of linear system. It is assumed that the state information of all following agents cannot be obtained directly, but only its output information can be obtained. Two types of linear functional observers are proposed for the following agents to estimate its state feedback inputs, by which two kinds of distributed consensus protocols are constructed to solve the leader-following consensus problem. Based on the graph theory, matrix theory and Lyapunov theory, some consensus conditions are established. The related consensus stability problem is investigated by use of the piecewise Lyapunov functions incorporated with the average dwell time approach. It is shown that if the average dwell time is chosen sufficiently large and all directed switching topologies have a directed spanning tree, then the multi-agent system can achieve consensus via the proposed protocols. Finally, a simulation example is provided to illustrate the effectiveness of our proposed approach.