Consensus of discrete-time linear multi-agent systems with observer-type protocols

This paper concerns the consensus of discrete-time multi-agentsystems with linear or linearized dynamics. An observer-typeprotocol based on the relative outputs of neighboring agents isproposed. The consensus of such a multi-agent system with a directedcommunication topology can be cast into the stability of a set ofmatrices with the same low dimension as that of a single agent. Thenotion of discrete-time consensus region is then introduced andanalyzed. For neurally stable agents, it is shown that there existsan observer-type protocol having a bounded consensus region in theform of an open unit disk, provided that each agent is stabilizableand detectable. An algorithm is further presented to construct aprotocol to achieve consensus with respect to all the communicationtopologies containing a spanning tree. Moreover, for the case wherethe agents have no polesoutside the unit circle,an algorithm is proposed to construct a protocol having anorigin-centered disk of radius $\delta$ ($0<\delta<1$) as itsconsensus region. Finally, the consensus algorithms are applied tosolve formation control problems of multi-agent systems.