Anti‐disturbance resilient tracking control for semi‐Markov jumping systems

摘要

Abstract This article investigates the output tracking problem of semi‐Markov jump systems with exogenous disturbance and generally uncertain transition probability rates. In particular, the elements in the transition rates are allowed to be known, uncertain or completely unknown. In specific, a state‐space of the modified repetitive controller is considered for tracking the given reference signals. Then, a generalized extended state observer is constructed to estimate the external disturbances and these estimates are incorporated in the control law to reject the disturbances effectively. Moreover, additive gain fluctuations are considered in the control design to tolerate gain fluctuations. First, a continuous‐discrete two‐dimensional (2D) delayed system is developed based on the lifting technique to characterize the repetitive control system's control and learning behavior. Then a sufficient condition for the bounded stability of the 2D hybrid system is obtained by choosing a suitable Lyapunov–Krasovskii functional. In addition, the control and observer gains are evaluated by solving a set of linear matrix inequalities and using the pole placement technique. At last, a robot arm model is presented to show the applicability of the proposed control scheme and a comparison study is made over some existing literature.