Structure identification of fuzzy model
Fuzzy Sets and Systems
Stability analysis and design of fuzzy control systems
Fuzzy Sets and Systems
Analysis and design of fuzzy control system
Fuzzy Sets and Systems
Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach
Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach
Guaranteed cost control of polynomial fuzzy systems via a sum of squares approach
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
A triangulation approach to asymptotically exact conditions for fuzzy summations
IEEE Transactions on Fuzzy Systems
Polynomial fuzzy models for nonlinear control: a Taylor series approach
IEEE Transactions on Fuzzy Systems
Stability analysis of fuzzy control systems subject to uncertain grades of membership
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
An approach to fuzzy control of nonlinear systems: stability and design issues
IEEE Transactions on Fuzzy Systems
Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs
IEEE Transactions on Fuzzy Systems
Fuzzy descriptor systems and nonlinear model following control
IEEE Transactions on Fuzzy Systems
New approaches to relaxed quadratic stability condition of fuzzy control systems
IEEE Transactions on Fuzzy Systems
On relaxed LMI-based designs for fuzzy regulators and fuzzy observers
IEEE Transactions on Fuzzy Systems
Approaches to quadratic stability conditions and H∞ control designs for T-S fuzzy systems
IEEE Transactions on Fuzzy Systems
A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems
IEEE Transactions on Fuzzy Systems
A Survey on Analysis and Design of Model-Based Fuzzy Control Systems
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
Automatica (Journal of IFAC)
New approaches to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI
Automatica (Journal of IFAC)
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This paper presents stability analysis of polynomial fuzzy-model-based (FMB) control systems using the sum-of-squares (SOS) approach. Recently, stability analysis of the polynomial fuzzy-control systems, which is a generalized form of the well-known Takagi-Sugeno (T-S) FMB control systems, has been reported in the form of SOS-based stability conditions. Lack of information on the relations between membership functions and premise variables, in the existing stability analysis approaches, causes conservatism of their results. In this paper, to derive relaxed stability conditions for polynomial FMB control systems, membership functions which are approximated with polynomials and carrying relations between membership functions and premise variables are brought into the stability analysis. Considering a polynomial FMB control system and based on the Lyapunov stability theory, stability conditions in the form of fuzzy summations are derived, where each term contains product of membership functions of the polynomial fuzzy model and polynomial fuzzy controller. Each product term is approximated by a polynomial. In order to obtain better approximation, the operating domain of membership functions is partitioned to subregions. Then, SOS-based stability conditions for all subregions are derived. Unlike some published stability-analysis approaches, the proposed one can be employed for stability analysis of polynomial fuzzy-control systems under imperfect premise matching of which the fuzzy model and fuzzy controller do not share the same membership functions. The solution of the SOS-based stability conditions can be found numerically using SOSTOOLS, which is a free third-party MATLAB Toolbox. Numerical examples are given to illustrate the effectiveness of the proposed stability conditions.