Design of stable fuzzy controller for non-linear systems subject to imperfect premise matching based on grid-point approach

This study investigates the systems stability of fuzzy-model-based (FMB) control systems. Based on the T-S fuzzy model representing the non-linear system, a fuzzy controller using grid-point (GP) technique is proposed to close the feedback loop. A GP is defined as the sub-operating domain of the non-linear system. For each GP, a corresponding GP fuzzy controller is employed to control the system. As the non-linearity in each GP is lower compared to that of the full operating domain, it is in favour of yielding relaxed stability analysis result using the GP control technique of which the nature of the membership functions and operating domain are taken into account. Furthermore, unlike most of the fuzzy control approaches, the proposed one can be applied to FMB control systems subject to imperfect premise matching that the fuzzy model and fuzzy controller do not share the same premise membership functions. As a result, some simple membership functions can be employed for the fuzzy controllers to lower the implementation cost. Based on the Lyapunov stability theory, stability conditions in terms of linear matrix inequalities are derived to guarantee the system stability and facilitate the controller synthesis. Simulation examples are given to demonstrate the merits of the proposed FMB control scheme using the proposed GP technique.