New stability criterion using a matrix-based quadratic convex approach and some novel integral inequalities

This study is concerned with the stability of a linear system with an interval time-varying delay. First, a new augmented Lyapunov–Krasovskii functional (LKF) is constructed, which includes three integral terms in the form of t t−h(h − t + s)j x˙TRjx˙(s) ds (j = 1, 2, 3). Second, three novel integral inequalities are established to estimate the upper bounds of the integrals tt−h(h − t + s)j x˙TRjx˙(s) ds (j = 0, 1, 2) appearing in the derivative of the LKF. Third, a matrix-based quadratic convex approach is introduced to prove not only the negative definiteness of the derivative of the LKF along with the trajectory of the system, but also the positive definiteness of the LKF. Finally, a novel delay-derivative-dependent stability criterion is formulated. The effectiveness of the stability criterion is shown through two numerical examples.