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This paper presents improved stability results by introducing a new delay partitioning method based on the theory of geometric progression to deal with T–S fuzzy systems in the appearance of interval time-varying delays and nonlinear perturbations. A common ratio    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$\alpha$$\end{document}   αis applied to split the delay interval into multiple unequal subintervals. A modified Lyapunov–Krasovskii functional (LKF) is constructed with triple-integral terms and augmented factors including the length of every subintervals. In addition, the recently developed free-matrix-based integral inequality is employed to combine with the extended reciprocal convex combination and free weight matrices techniques for avoiding the overabundance of the enlargement when deducing the derivative of the LKF. Eventually, this developed research work can efficiently obtain the maximum upper bound of the time-varying delay with much less conservatism. Numerical results are conducted to illustrate the remarkable improvements of this proposed method.

Improved results on nonlinear perturbed T–S fuzzy systems with interval time-varying delays using a geometric sequence division method