Exponential stability of integral time-varying delay system

Abstract

This paper investigates exponential stability problem of integral time-varying delay system. Based on a novel exponential stability theorem, sufficient conditions for exponential stability of integral time-varying delay system are obtained in the form of coupled linear matrix inequalities (LMIs). These sufficient stability conditions cover some previous results as special cases when the integral time-varying delay system reduce to the integral time-invariant delay system. These sufficient conditions cannot be obtained directly from Theorem 1 given in Li, Zheng, and Wang [(2016). Exponential stability analysis of integral delay systems with multiple exponential kernels. Journal of the Frankline Institute, 353, 1639–1653. https://doi.org/10.1016/j.jfranklin.2015.12.016] due to the presence of time-varying delays. This is the main motivation for the research being carried out in this paper. Four example s are provided to show the effectiveness and advantages of the proposed method.

Keywords:

• Integral system
• time-varying delay
• exponential stability
• Lyapunov–Krasovskii functional (LKF)

Acknowledgments

The authors thank the anonymous referees for their helpful comments and suggestions, which greatly improved this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 12101144], the Australian Research Council [grant number DP190103361], the Innovation and Entrepreneurship Education Research Fund of Guangxi Normal University [grant numbers CXCYSZ2021009, CXCYSZ2021012], Humanities & Social Sciences research Center of Guangxi [grant number LJGD202005], Guangxi Science and Technology Planing Project [grant numbers 2018AD19211, 2019AC20186].