Stability analysis of linear delayed systems based on an allowable delay set partitioning approach

Abstract

This note is concerned with the stability analysis of linear systems with a time-varying delay, where the delay is assumed to be a periodically varying bounded function with restricted derivatives. Combining the allowable delay set (ADS) definition and the region partitioning technique, an ADS partitioning approach is proposed, and then by with aid of this approach, a novel Lyapunov–Krasovskii functional (LKF), namely delay-set-partition-based (DSPB) LKF, is developed. Compared with the previous LKF method, the main advantage of the DSPB LKF lies in allowing the considered system to construct its own LKF in each sub-ADS. By utilizing the proposed LKF, less conservative stability criteria are derived. Finally, two simulation examples are provided to verify the effectiveness and superiority of the proposed method.