Stability Analysis for Time-delay Systems via a Novel Negative Condition of the Quadratic Polynomial function

This paper studies the stability analysis problem for time-varying delay systems. An appropriate Lyapunov-Krasovskii functional (LKF) is constructed where its derivative is a quadratic polynomial function of the delay. A novel negative condition of the mentioned quadratic function with two variable parameters is developed to ensure that the LKF derivative is negative, reducing conservatism on some similar results. Besides, an extended version of Bessel-Legendre inequality is introduced to be employed in the stability analysis of time-varying delay systems. Then, some stability criteria with less conservatism are derived for two kinds of the time-varying delay. Finally, the effectiveness of the proposed stability criteria is demonstrated through three examples.