Stability analysis and design of fuzzy control systems
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
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
Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
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This paper presents stability analysis of polynomial fuzzy control systems using Sum-Of-Squares (SOS) approach. To take continuous form of membership functions into the stability analysis, based on the Lyapunov stability theory, stability conditions in the form of fuzzy summations are derived where each term contains product of polynomial fuzzy model and polynomial fuzzy controller membership functions. Then each product term is approximated by polynomials in the partitioned operating domain of membership functions. Regarding to the derived conditions in all sub-regions, SOS-based stability conditions are formed. The proposed approach can be utilized for stability analysis of polynomial fuzzy control system in which fuzzy model and fuzzy controller do not share the same membership functions named non-PDC design technique. The solution of the SOSbased stability conditions can be found numerically using the SOSTOOLS which is a free third-party MATLAB Toolbox. Numerical example is given to illustrate the effectiveness of the proposed stability conditions.