Robust stabilization of linear plants in presence of disturbances and high-frequency measurement noises

A solution is proposed for the robust stabilization of linear dynamic plants with unknown parameters belonging to a known compact set, bounded external disturbances, and bounded high-frequency measurement noises. The synthesis of the control algorithm is divided into two steps. At the first step a filtering algorithm is synthesized, which makes it possible to reduce the influence of measurement noises on the output variable of the plant. If the measurement noises can be represented as the sum of sinusoidal signals, then constructive conditions for choosing parameters in the filtering algorithm are proposed. At the second step, a control algorithm is synthesized with the attenuation of the influence of parametric uncertainty and external disturbances. This algorithm is based on the use of finite differences in continuous time, which avoids the use of dynamic observers that increase the dimension of a closed-loop system. The simulation results illustrating the effectiveness of the proposed algorithm in comparison with some existing analogues are presented. Thus, a comparative analysis with the results of Astolfi D., Marconi L., Isidori A. etc. has been showed that the proposed control algorithm have less dynamic order, guarantees higher accuracy with respect to the output signal and its derivatives. Moreover, in contrast to the results of Astolfi D., Marconi L., Isidori A. etc., in the proposed algorithm, choosing the algorithm parameters is easier due to independent filter settings and the control law, while choosing parameters in the controller of Astolfi D., Marconi L., Isidori A. etc. performed simultaneously for the whole algorithm.