Improved stability criteria for nonlinear fractional order fuzzy systems with time-varying delay

This paper addresses the issue of the stability analysis and stabilization of nonlinear time-delayed systems with fractional order α∈0,1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha \in \left( {0,1} \right)$$\end{document} modeled by Takagi–Sugeno fuzzy model. A new Lyapunov-Krasovskii functional is proposed based on Caputo derivative which leads to obtaining less conservative stability conditions are proposed. Both approaches state feedback and delayed state feedback are applied in the form of a parallel-distributed compensation scheme for stabilization of the closed-loop system. Each of the stability conditions is written as a linear matrix inequality. Finally, some examples are presented to illustrate the effectiveness of the proposed approach.