A Novel Convexification Method for Control Synthesis Analysis of Continuous-Time Saturated Positive Polynomial Fuzzy Systems Under Imperfect Premise Matching

Meng Han, Yongjie Huang, Ge Guo, Hak-Keung Lam, Zhengsong Wang, Liangliang Sun

Abstract: This paper investigates the polynomial fuzzy controller design methodology for continuous-time positive polynomial fuzzy (PPF) systems to enlarge their feasible area. An improved Chebyshev membership function-dependent (MFD) convexification method is proposed to handle the nonconvex stability conditions and positivity conditions. Compared with the previous MFD convexification method, this improved convexification method removes the positive restriction imposed on the slack matrices, so it reduces the conservatism of the analysis results and helps to expand the system feasible area. In addition, this improved convexification method can also be extended to the saturated PPF systems (SPPF), and together with the convexification method proposed for the nonconvex estimation conditions of the polyhedron domain of attraction (DOA), the more relaxed results can be derived to obtain a larger estimation of DOA. In both cases, without and with input saturation constraints, a numerical example is used to illustrate the usefulness of the proposed controller design methodology and novel convexification methods in enlarging the feasible area and estimation of DOA.

External IDs:dblp:journals/ijfs/HanHGLWS25