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Model-based fuzzy controller design for time-delay affine Takagi-Sugeno fuzzy models via ILMI algorithm

Recently, the Takagi-Sugeno T-S fuzzy model has become one of the most useful control approaches for complex systems. It provides an effective representation of complex nonlinear systems in terms of fuzzy sets. In this paper, the stability and stabilization issues of continuous time-delay affine T-S fuzzy models are presented. Based on Lyapunov stability criterion and Razumikhin theorem, an Iterative Linear Matrix Inequality ILMI algorithm is used to solve the Bilinear Matrix Inequalities BMI problem. Also, ILMI can be used to find feasible solutions for the synthesis of the continuous time-delay affine T-S fuzzy models. Finally, a numerical simulation for a delayed inverted pendulum system is given to show the applications of the present approach.