Improved Extended Dissipativity Results for T-S Fuzzy Generalized Neural Networks With Mixed Interval Time-Varying Delays

The asymptotic stability and extended dissipativity performance of T-S fuzzy generalized neural networks (GNNs) with mixed interval time-varying delays are investigated in this paper. It is noted that this is the first time that extended dissipativity performance in the T-S fuzzy GNNs has been studied. To obtain the improved results, we construct the Lyapunov-Krasovskii functional (LKF), which consists of single, double, triple, and quadruple integral terms containing full information of the delays and a state variable. Moreover, an improved Wirtinger inequality, a new triple integral inequality, and zero equation, along with a convex combination approach, are used to deal with the derivative of the LKF. By using Matlab’s LMI toolbox and the above methods, the new asymptotic stability and extended dissipativity conditions are gained in the form of linear matrix inequalities (LMIs), which include passivity, $L_{2}-L_{\infty }$ , $H_{\infty }$ , and dissipativity performance. Finally, numerical examples that are less conservative than previous results are presented. Furthermore, we give numerical examples to demonstrate the correctness and efficacy of the proposed method for asymptotic stability and extended dissipativity performance of the T-S fuzzy GNNs, including a particular case of the T-S fuzzy GNNs.