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Output Feedback and Stability Analysis of Positive Polynomial Fuzzy Systems

This article investigates the polynomial fuzzy output feedback (PFOF) control synthesis problem for positive polynomial fuzzy systems. When the states of a positive system cannot be fully obtained, the output feedback control strategy is a good method to stabilize the control system. From fuzzy control point of view, we employ the polynomial fuzzy model rather than the Takagi–Sugeno fuzzy model, and this kind of models can express a wider range of nonlinear positive systems. However, the polynomials in the system matrices and the feedback control gain matrices will make the nonconvex stability conditions more difficult to deal with. Thereby, in order to crack the hard nut, a nonzero transformation vector is introduced in this article to deal with the nonconvex problem skillfully. Furthermore, the imperfect premise matching technique is taken into account so that the implement of the controller is more simple and money-saving. In addition, the augmented dynamic of the positive polynomial fuzzy-model-based (PPFMB) control system is investigated to facilitate the stability and positivity analysis, and the basic conditions in the light of sum of squares (SOSs) are derived. Besides, the advanced membership function dependent (MFD) technique is used so that a great of useful information of MFs is extracted to improve the relaxation of the results. Finally, the effectiveness of the theoretical findings is illustrated by a simulation example.