Robust Stabilization of Linear Plants in the Presence of Disturbances and High-Frequency Measurement Noise

We propose a solution of the robust stabilization problem for linear dynamic plants with unknown parameters belonging to a known compact set, bounded exogenous disturbances, and bounded high-frequency measurement noise. The control algorithm synthesis is divided into two stages. The filtering algorithm synthesized at the first stage permits one to reduce the influence of the measurement noise on the plant output variable. Constructive conditions for selecting the filtering algorithm parameters are proposed for the case in which the measurement noise can be represented as a sum of sinusoidal signals. At the second stage, we synthesize a control algorithm suppressing the influence of the parametric uncertainty and exogenous disturbances. This algorithm is based on the use of finite differences in continuous time; this allows avoiding the use of dynamic observers increasing the dimension of the closed-loop system. Simulation results illustrating the efficiency of our algorithm in comparison with some existing analogs are presented. A comparative analysis with the results by Astolfi et al. has shown that our control algorithm has lower dynamic order and guarantees higher accuracy in the output signal and its derivatives. Moreover, the algorithm parameter selection in our algorithm is easier owing to the independent adjustment of the filter and control law in contrast to the results by Astolfi et al., where the controller parameters are selected simultaneously for the entire algorithm.