Further Improved Wirtinger Inequalities Approach to Stability of Systems with Time-Varying Delays

This paper develops a further improved Wirtinger inequality to derive stability condition of time-varying-delay systems based on an approximate inequality. Then, applying the inequality to three class of systems with time-varying-delay, some original delay-dependent criteria is obtained by utilizing Lyapunov- Krasovskii functional. The analysis shows that the new inequality can further reduce the conservativeness compared to other methods. Moreover, the further improved Wirtinger inequality achieves a high-order approximation. Finally, some numerical examples are given to illuminate the effectiveness and superiority of the proposed method.