Consensus with distributed LQR control algorithm for discrete-time multi-agent systems

In this paper, the distributed consensus problem with a performance index coupling the behavior between the multi-agents for discrete-time identical scalar subsystems has been investigated. Assuming a time-invariant undirected network topology for the multi-agents, we first present a suboptimal design method with the aid of the decomposition of discrete algebraic Riccati equations and robustness of local controllers. Then by constructing the gain matrix which with two parameters, the consensus problem presents the property the same as the condition for distributed optimal controller was proposed based-on the form of optimal control. The structure of the penalty matrix related to state is selected under the condition of the asymptotically stable and the final state of the multi-agents system is obtained.