According to mathematical properties of continuous function, the universal approximation properties of fuzzy mapping in only one interval are analyzed, and some related theorems are proposed and proved. Then, the sufficient conditions of the general T-S fuzzy systems with universal approximation are derived from these theorems, which helps establish the new relationship between approximation er...

In recent years, the Takagi–Sugeno (T–S) fuzzy model has been commonly used for the approximation of nonlinear systems. Using the T-S fuzzy model, nonlinear systems can be converted into linear time-varying systems, which can reduce approximation errors compared with the conventional Taylor approximation. In this paper, we propose a new nonlinear filter with a finite impulse response (FIR) stru...

Takagi–Sugeno (T–S) fuzzy models play an important role in nonlinear control because they can be used to approximate nonlinear systems. Also, for the affine T–S fuzzy models, the local linear sub-system properties can be easily related to the physics of the controlled nonlinear system. This is one advantage of the affine T–S fuzzy models relative to the homogeneous T–S fuzzy models. In the lite...

This paper addresses the criterion of delay-dependent stability for nonlinear systems with time-delays which can be represented by Takagi–Sugeno (T–S) fuzzy model with time-delays. Based on Leibniz-Newton formula, the e¤ect of states and the delay states to the stability is considered to construct a Lyapunov functional and to form some special equations, which facilitate proposing a new delay-d...

Fuzzy control has achieved numerous successful industrial applications. However, stability analysis for fuzzy control systems remains a difficult problem, and most of the critical comments on fuzzy control are due to the lack of a general method for its stability analysis. Although significant research efforts have been made in the literature, appropriate tools for this issue have yet to be fou...

Controller design strategy for Takagi-Sugeno (T-S) fuzzy systems is considered in the two-degree-of-freedom (TDOF) framework. Firstly, coprime factorization described in the state space formulas for T-S fuzzy systems is introduced based on a common Lyapunov function. Secondly, based on this coprime factorization, TDOF framework for LTI systems is extended to be applied to T-S fuzzy systems. Con...

Fuzzy systems can provide us with universal approximation models of deterministic input–output relationships, but in the stochastic environment few achievements related to the subject have so far achieved. In the paper a novel stochastic Takagi–Sugeno (T–S) fuzzy system is introduced to represent approximately existing randomness in many real-world systems. By recapitulating the general archite...

In this work, three topics which are important for the further development of fuzzy systems are chosen to be investigated. First, the mathematical aspects of fuzzy relational equations (FREs) are explored. Solving FREs is one of the most important problems in fuzzy systems. In order to identify the algebraic information of the fuzzy space, two new tools, called fuzzy multiplicative inversion an...

This article presents a fuzzy sliding-mode control scheme for a class of Takagi-Sugeno (T-S) fuzzy which are subject to norm-bounded uncertainties in each subsystem. The proposed stabilization method can be adopted to explore T-S uncertain fuzzy systems (TSUFS) with various local control inputs. Firstly, a new design is proposed to transform TSUFS into sliding-mode dynamic systems.In addi...