This paper focuses on the guaranteed cost stability analysis of fuzzy-model-based (FMB) control systems. Representing the nonlinear plant using a Takagi–Sugeno (T–S) fuzzy model, a fuzzy controller is employed to close the feedback loop. A weighted linear quadratic cost function is considered as the cost index to measure the performance of the closed-loop fuzzy system in terms of the system states, system outputs, and control signals. The stability of the FMB control system is investigated by the Lyapunov stability theory subject to the minimization of cost index for performance realization. A membership-function-dependent approach using the piecewise-linear membership functions is employed to include the information of membership functions into the stability analysis. Membership-function-dependent stability conditions in terms of linear matrix inequalities are obtained to determine the system stability and feedback gains with the consideration of the system performance measured by the cost function. A simulation example is provided to illustrate the effectiveness and merits of the proposed approach.

In this article, the reconstruction error between a real system to be controlled and its Takagi–Sugeno (T-S) fuzzy model is considered in the context of control system design. Accordingly, we propose an H _∞ approach to an adaptive controller that consists of two parts: one is obtained by solving certain linear matrix inequalities (fixed part) and the other is acquired using a fuzzy approximator in which the related parameters are tuned by an adaptive law (variable part). The proposed controller can guarantee a convergent and uniformly bounded control state while maintaining the stability of all the signals involved.

This paper deals with stability analysis and control design for a class of nonlinear systems with input constraint when using T-S fuzzy model. After leading the control design to LMIs approach, the attention is paid to: (1) how to easy the LMIs conditions so that the system is asymptotically stable in a so-called ellipsoid to be made as large as possible; (2) how to relax the LMIs conditions so that the LMIs problem is more feasible. Also a few examples are given to illustrate the theoretical analysis.

Title: A Design of Observers of Control State and Uncertainty via Transformation of T-S Fuzzy Models | Keywords: T-S fuzzy model, uncertainty, state observer, uncertainty observer, matrix transformation | Author: Hugang Han, Yuki Sueyama, and Chun-Jun Chen