Optimal tracking control for discrete-time systems with delayed state and input

The optimal tracking control for discrete-time systems with delayed state and input is addressed. By introducing a function-based transformation, the discrete time-delay system is transformed into a non-delayed system. The optimal tracking controller is constructed by the solution of a Riccati matrix equation and a Stein matrix equation. A reduced-order observer is constructed to solve the physically realizable problem of the feedforward compensator. Simulation results demonstrate the effectiveness of the optimal tracking control law.