Observer-based state tracking control of uncertain stochastic systems via repetitive controller

This paper develops the repetitive control scheme for state tracking control of uncertain stochastic time-varying delay systems via equivalent-input-disturbance approach. The main purpose of this work is to design a repetitive controller to guarantee the tracking performance under the effects of unknown disturbances with bounded frequency and parameter variations. Specifically, a new set of linear matrix inequality (LMI)-based conditions is derived based on the suitable Lyapunov–Krasovskii functional theory for designing a repetitive controller which guarantees stability and desired tracking performance. More precisely, an equivalent-input-disturbance estimator is incorporated into the control design to reduce the effect of the external disturbances. Simulation results are provided to demonstrate the desired control system stability and their tracking performance. A practical stream water quality preserving system is also provided to show the effectiveness and advantage of the proposed approach.