Robust integral sliding mode regulator for linear systems with time delay in control input

The paper presents a robustification algorithm for the obtained optimal regulator based on integral sliding mode compensation of disturbances. The general principles of the integral sliding mode compensator design, which yield the basic algorithm applied then to robustify the optimal regulator, are outlined. As a result, the sliding mode compensating control leading to suppression of the disturbances for a finite time is designed. This control algorithm also guarantees finite-time convergence of the disturbed state to the optimally controlled one. The obtained robust control algorithm is verified by simulations in the illustrative example.