Stability Analysis for Linear Systems with Time-Varying Delay via Combined Convex Technique

This paper is concerned with the problem of stability analysis of linear systems with time-varying delay. A new delay-dependent stability condition expressed in terms of linear matrix inequalities (LMIs) is derived by employing a dedicated constructed Lyapunov-Krasovskii functional (LKF) and combining a novel combined convex method. Different from the previous convex techniques which only tackle the time-varying delay, our method applies the idea of combined convex technique which can tackle not only the delay but also delay variation. Two well known examples are illustrated to show the effectiveness of the proposed results.