Improved sliding mode observer based repetitive control for linear systems with time-varying input and state delays

Control systems are frequently subject to the negative effects of time delays and disturbances, which diminish the systems' tracking performance. In response to these challenges, this paper presents a novel approach, that is, the improved sliding mode observer based repetitive control (ISMO-RC), to enhance the system's periodic signal tracking in the presence of the input and state time delays and the input disturbances. The design takes the advantages of RC and ISMO, in which RC effectively compensates periodic signals, while ISMO compensates both aperiodic disturbances and the time-varying input and state delays. The stability of the whole system is guaranteed via the linear matrix inequality (LMI) and the Lyapunov-Krasovskii functional analysis. The proposed controller is evaluated through extensive simulations and experiments, which demonstrate its superiority over comparative control methods.