Distributed LQR control for scalar discrete-time uncoupled identical systems

This paper investigates the distributed LQR problem for the scalar identical discrete-time multiple systems. Based on the optimal centralized control, the existence condition for the distributed optimal control is first proposed. It reveals that the globally optimal distributed controller is dependent on the structure of the penalty matrix related to the state. When the proposed condition cannot holds, an suboptimal design method with the aid of the decomposition of the discrete algebraic Riccati equations and robustness of the local controllers is also proposed by using the Riccati equation decomposition approach.