Stability Analysis for Linear Systems with a Differentiable Time-Varying Delay via Auxiliary Equation-Based Method

This paper concentrates on the stability problem for linear systems with a differentiable time-varying delay via an auxiliary equation-based method. By supposing that second-order derivative of system state is available, equation obtained. On basis and equation, we define suitable delay-product-type augmented Lyapunov-Krasovskii functional (LKF), under which more information can be exploited. Based LKF, by utilizing some vital lemmas, adding zero terms, convex analysis method, propose new condition less conservative. Finally, to illustrate merit obtained condition, two typical numerical examples are given.