Consensus of Linear Singular Multi-agent Systems Based on State Feedback Approach

In this paper, the consensus problem for singular multi-agent systems is studied with a fixed communication topology consisting of general singular linear dynamics. Based on the local relative state information, a distributed consensus protocol is proposed. It is shown that there exists a consensus protocol solving the consensus problem and meanwhile yielding an unbounded consensus region if and only if each singular agent is both stabilizable and detectable. The Lyapunov theory is used as fundamental tools to establish the stability of the closed-loop system. It is shown that the formation control objective can be achieved if a spanning tree condition is satisfied by the interconnection topology. Finally, the effectiveness and superiority of the proposed method are illustrated by a numerical example.