Output feedback optimal control for MIMO systems with external disturbances based on observer

This paper considers the optimal output feedback control problem for MIMO (Multiple Input Multiple Output) systems affected by external disturbances. The optimal disturbance rejection control law in finite-time and infinite horizon form are first proposed by using the solutions of a Riccati equation and a Sylvester equation. We give the existence and uniqueness conditions of the optimal output law, and construct an observer to estimate the state variables x(t), by using the signal of input variables u(t) and output variables y(t). Then we achieve the optimal disturbances rejection control law by using the estimated value of state variable for feedforward and feedback control. Finally, a practical example is given to illustrate the effectiveness of the theory.