Robust Compensation of External Disturbances for A Class of Linear Systems with State-Delay

The problem of unknown external disturbances compensation for a class of linear systems with an unmeasured and delayed state is considered. The proposed solution is based on the use of the internal model principle and the extended error adaptation algorithm. It is assumed that the disturbance is the output of an autonomous linear generator with unknown parameters. A special observer is constructed to estimate the disturbance. The proposed approach does not require identification of the disturbance parameters. It is shown that in the presence of any state delay, the control algorithm preserves the stability of the closed-loop system. The performance of the obtained result is confirmed using computer simulation.