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 a quadratic polynomial function of delay. A novel negative condition mentioned with two variable parameters developed to ensure that LKF negative, reducing conservatism on some similar results. Besides, an extended version Bessel-Legendre inequality introduced be employed in Then, criteria less are derived kinds Finally, effectiveness proposed demonstrated through three examples.