Delay-dependent robust stability and stabilization for polytopic systems with time-varying delay

The paper addresses robust stability and stabilization for continuous time-delay systems with polytopic uncertainty. The delay is assumed time-varying with both its value and variation rate being bounded. Based on a new Lyapunov-Krasovskii functional and the application of delay partitioning and the Jensen inequality techniques, a set of sufficient LMI conditions is obtained to ensure the asymptotical stability of a nominal system. Since there is no product term of Lyapunov matrix with any system matrix, the extension to cope with polytopic uncertainty is straightforward. The robust stabilization problem of computing a state feedback gain is also solved. Numerical examples are given to show the effectiveness and the improvement of the derived results.