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