Stability Analysis of Systems With Time-varying Delay via a Novel Lyapunov Functional

This paper investigates the stability problem for time-varying delay systems. To obtain a larger delay bound, this paper uses the second-order canonical Bessel-Legendre (BL) inequality. Secondly, using four couples of integral terms in the augmented Lyapunov-Krasovskii function (LKF) to enhance the relationship between integral functionals and other vectors. Furthermore, unlike the construction of the traditional LKF, a novel augmented LKF is constructed with two new delay-product-type terms, which adds more state information and leads to less conservative results. Finally, two numerical examples are provided to demonstrate the effectiveness and the significant improvement of the proposed stability criteria.