On Delay-Dependent Robust Stability for Uncertain Systems with Time-Varying Delays

This paper discusses the issue of delay-dependent robust stability for uncertain linear systems with time-varying delays and norm-bounded uncertainties. A new sufficient condition is obtained by employing a Lyapunov-Krasovskii functional (LKF). This LKF considers the cross terms between x(s) and x(s) in both single and double integrals. Both model transformation and estimating techniques for cross terms are not involved in the derivation, and no slack matrices are introduced. The proposed criterion is based on Jensen inequality and formulated in terms of linear matrix inequalities (LMIs). Some numerical examples are provided to demonstrate the effectiveness of our methodology.