Matrix Quadratic Convex Combination for Stability of Linear Systems with Time-Varying Delay via New Augmented Lyapunov Functional

The paper addresses the delay-dependent stability problem for linear systems with time-varying delay. Novel delay-dependent stability criteria in terms of linear matrix inequalities for systems with state time-varying delay are derived by the newly proposed augmented Lyapunov-Krasovski (L-K) functional. A matrix-type quadratic convex combination approach is introduced to prove the negative definiteness of the derivative of the L-K functional along with the trajectory of the delayed system. Different from previous results by using the first order convex combination, our derivation applies the idea of second order convex combination, and the property of quadratic convex function without resorting to the Jensen's inequality.