Finite-Time Stability Analysis and Control Design of Interval Type-2 Polynomial Fuzzy Positive Systems

This paper focuses on the finite-time stabilization of interval type-2 (IT2) fuzzy polynomial positive systems. For the purpose of stability analysis, an IT2 fuzzy co-positive Lyapunov function (FCLF) is designed, which inevitably generates a term with the derivative of the membership functions (MFs) of the IT2 FCLF. In dealing with this term, unlike most previous studies which only consider the boundary information of the derivative of the MFs of the IT2 FCLF, this paper also introduces the nature of the derivative of the MF. While the proposed IT2 FCLF gives more relaxed stabilization results, it also leads to more complicated non-convex problems. To solve this difficulty, the matrix decomposition technique is used to design the feedback control gains of IT2 fuzzy polynomial controllers. Moreover, if the information of the MFs is ignored, the results obtained will be very conservative. In order to reduce conservatism, an improved piecewise linear approximation method is proposed. It offers a novel perspective on approximating MFs, facilitating the incorporation of more valuable information, such as the approximation errors, into the stability conditions so that the relaxation of the stability analysis results can be enhanced. Finally, a simulation example verifies the effectiveness of the proposed strategy.