New fractional-order integral inequalities: Application to fractional-order systems with time-varying delay

In this paper, the problem of delay-dependent stability analysis of fractional-order systems with timevarying delay is investigated. First, a class of novel fractional-order integral inequalities for quadratic functions by constructing appropriate auxiliary functions is proposed, which has been proven to be useful in analyzing fractional-order systems with time-varying delay. Based on these proposed inequalities, the Lyapunov?Krasovskii functions are designed to deal with the time-varying delay terms, reducing the conservatism of the stability criteria. Furthermore, delay-dependent criteria are derived to achieve asymptotic stability of fractional-order systems with time-varying delay. Finally, two examples are provided to illustrate the effectiveness and feasibility of the proposed stability criteria. ? 2021 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates the delay-dependent stability analysis of fractional-order systems with time-varying delay by proposing novel fractional-order integral inequalities and designing Lyapunov-Krasovskii functions to reduce conservatism, deriving delay-dependent criteria to achieve asymptotic stability of systems with time-varying delay.