Optimal sliding mode vibration control for systems with delayed state and control

The problem of optimal vibration control for time-delay systems is considered by using the sliding mode control approach. The delayed system is transformed into a non-delayed one by using functional transformations. The optimal sliding surface and the sliding controller are derived from a Riccati equation and a Sylvester equation. The feedforward control compensates for the effect of disturbance. The state and control memory terms are designed to compensate the effect of the state and control delays, respectively. A disturbance observer is constructed to make the controller physically realizable. Simulation results illustrate the effectiveness of the proposed controller.