Improved results on stability analysis of time-varying delay systems via delay partitioning method and Finsler's lemma

This paper proposes novel conditions based on linear matrix inequalities (LMI) for stability analysis of arbitrarily-fast time-varying delays systems. The time-varying delay interval is divided into smaller pieces in order to obtain an equivalent switched model with multiple time-varying delays of smaller interval, which differently from other existing approaches, the maximum switching frequency is not required for stability analysis. Thus, by the use of augmented Lyapunov-Krasovskii functionals and the Finsler's lemma, together with some relationships among state variables intentionally defined, the inherent conservatism can be progressively reduced by refining more and more the delay partition. The superiority of the proposed method is illustrated through two benchmark examples. (C) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Automated summary

This paper proposes novel conditions based on linear matrix inequalities (LMI) for stability analysis of arbitrarily-fast time-varying delays systems. The time-varying delay interval is divided into smaller pieces in order to obtain an equivalent switched model with multiple time-varying delays of smaller interval, which eliminates the requirement for maximum switching frequency in stability analysis. By using augmented Lyapunov-Krasovskii functionals and the Finsler's lemma, and defining intentional relationships among state variables, the conservatism of the system can be progressively reduced by refining the delay partition. The superiority of the proposed method is demonstrated through two benchmark examples.