Non-monotonic fuzzy state feedback controller design for discrete Time T-S fuzzy systems

A review on stability analysis of continuous-time fuzzy-model-based control systems: From membership-function-independent to membership-function-dependent analysis

“…In the literature of FMB/PFMB control systems, the concept of higherorder Lyapunov function candidate is applied mainly in discrete-time systems [184,185,186,187,188,189,190] but much less in continuous-time systems [191] as the derivative terms of membership functions are far more difficult to be handled in continuous-time systems.…”

Design of Fuzzy Functional Observer-Controller via Higher Order Derivatives of Lyapunov Function for Nonlinear Systems

“…For brevity, the membership function w i (y) is denoted as w i . The estimation error is defined as e j = u j −ȗ j = G j x − (z j + E j y) = Q j x − z j , where Q j = G j − E j C, and then we have the closed-loop system consisting of the T-S fuzzy model (19), the fuzzy controller (20), and the fuzzy functional observer (21) as follows:…”

“…Consequently, the HODLF should be combined with FMB control scheme such that general nonlinear systems can be dealt with. In discrete-time FMB control system, the nonmonotonic Lyapunov function [20]- [22] and the multistep Lyapunov function were investigated [23]- [26]. Similar to HODLF, they involve the difference of Lyapunov function in more steps instead of only one step.…”

“…Second, the lower bound of the derivative of membership functions is allowed to be different from the upper bound, which leads to more relaxed conditions. Compared with existing work in discrete time [20]- [26], this is the first attempt to consider HODLF in continuous-time FMB control systems. Also, it can be demonstrated from the simulation that the proposed stability conditions from HODLF are more relaxed than those from the fuzzy Lyapunov function in [15] by comparing the stabilization region.…”