Equivalent‐input‐disturbance‐based repetitive tracking control for Takagi–Sugeno fuzzy systems with saturating actuator

This study investigates the output tracking problem for a class of Takagi–Sugeno fuzzy systems subject to periodic signals and actuator saturation via equivalent-input-disturbance (EID) technique. In particular, to ensure the periodic signals tracking, a state-space repetitive control structure is considered. Further, the EID technique is utilised to improve the disturbance rejection performance without any prior knowledge of the disturbance and inverse dynamics of the plant. By constructing a suitable Lyapunov–Krasovskii functional and using the Wirtinger-based integral inequality, a new set of sufficient conditions is derived in terms of linear matrix inequalities (LMIs) which ensures the stability of the addressed system. In addition to that by using a Lyapunov level set, saturation-dependent Lyapunov function captures the real-time information on the severity of actuator saturation and leads to less conservative estimate of the domain of attraction, which is based on the solution of an LMI optimisation problem. Moreover, the designed fuzzy repetitive controller is reliable in the sense that the stability and the satisfactory performance of the closed-loop system are achieved not only under normal operation, but also in the presence of any actuator faults, saturation and dead zone. Finally, the proposed method is validated through two numerical examples to illustrate the effectiveness and superiority of the developed controller design.