Delay-Dependent Robust Stability of Uncertain Hereditary Systems Involving Time-Varying State Delays

This note encompasses the robust stability of linear hereditary systems with state-delay. The delay is time-varying with arbitrary finite time evolution rate. The uncertainty taken into account is assumed to be of polytopic type. A less conservative delay-dependent linear matrix inequality (LMI) method is presented based on a new Lyapunov-Krasovskii functional. Descriptor model transformation has been used and a sufficient condition for the robust stability is presented. The result obtained includes information on the size of the delay, and is therefore a delay-dependent robust stability condition. The results are general and not restricted to time-delay systems with delay derivative less than unity. Illustrative numerical examples are given to reflect the effectiveness of our results