An Improved Augmented Delay Partitioning Approach for the Stability of Time-Varying State-Delayed Systems

This paper deals with the asymptotical stability problem of retarded type time-delay systems with time-varying delays using the technique of decomposing the delay interval uniformly into an integer number of equal size segments and proposing an appropriate Lyapunov-Krasovskii (L-K) functional to develop delay-dependent stability criteria. The novelty of the proposed method originates from two significant contributions. First, a quasi-full size augmented form of L-K functional is introduced for the stability analysis. Second, almost exact full information has been exploited for the relationship among the actual time-varying delay and its upper bound concerning the delay related integral terms. This approach allows to avoid any redundant enlargement with the delay upper bound while estimating the derivative of the L-K functional as it will bring naturally conservativeness on the results. Several numerical examples are taken into account with some case studies to illustrate the effectiveness of the proposed method. For the treated examples, the results of maximum admissible delay bound have clearly indicated that the proposed approach provides significant improvement over those reported in the literature.