On Stability and Stabilization of T–S Fuzzy Systems With Time-Varying Delays via Quadratic Fuzzy Lyapunov Matrix

This article proposes improved stability and stabilization criteria for Takagi–Sugeno (T–S) fuzzy systems with time-varying delays. First, a novel augmented fuzzy Lyapunov–Krasovskii functional (LKF) including the quadratic fuzzy Lyapunov matrix is constructed, which can provide much information of T–S fuzzy systems and help to achieve the lager allowable delay upper bounds. Then, improved delay-dependent stability and stabilization criteria are derived for the studied systems. Compared with the traditional methods, since the third-order Bessel–Legendre inequality and the extended reciprocally convex matrix inequality are well employed in the derivative of the constructed LKF to give tighter bounds of the single integral terms, the conservatism of derived criteria is further reduced. In addition, the quadratic fuzzy Lyapunov matrix introduced in LKF, which contains the quadratic membership functions, is also an important reason for obtaining less conservative results. Finally, numerical examples demonstrate that the proposed method is less conservative than some existing ones and the studied system can be well controlled by the designed controller.