Weight conditions for consensus of discrete-time multi-agent systems

This paper studies discrete-time general linear multi-agent systems over a fixed directed topology. Dynamic output feedback protocols are applied to solve the consensus problem. Being different from the low-order integrator and continuous-time systems, it is revealed that the solvability of the consensus depends on the weights of the topology. The consensus problem is converted to the simultaneous mean square stability of some stochastic switching subsystems. By considering the robust stability of certain system with uncertainty, a sufficient condition of the weights under which there exist dynamic output feedback protocols solving the consensus problem is given. Proper protocol parameters are further provided.