Input-to-state stability of delayed systems with bounded-delay impulses

Bangxin Jiang; Yijun Lou; Jianquan Lu; Bangxin Jiang; Yijun Lou; Jianquan Lu

doi:10.3934/mmc.2022006

Mathematical Modelling and Control

2022, Volume 2, Issue 2: 44-54. doi: 10.3934/mmc.2022006

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Research article

Input-to-state stability of delayed systems with bounded-delay impulses

1.
Department of Systems Science, School of Mathematics, Southeast University, Nanjing 210096, China
2.
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong, China

Received: 08 December 2021 Revised: 16 February 2022 Accepted: 06 March 2022 Published: 24 March 2022

This paper considers the input-to-state stability (ISS) of delayed systems with bounded-delay impulses, where the delays in impulses are arbitrarily large but bounded. A novel Halanay-type inequality with delayed impulses and external inputs is proposed to deeply evaluate the effects of delayed impulses on ISS of delayed systems. Then, we obtain some delay-independent ISS criteria for the addressed delayed systems by using Lyapunov method. Particularly, by applying a new analysis technique, the current study enriches the Halanay-type inequalities and further improve the results derived in ^[1]. Two illustrative examples are presented to validate theoretical results.
- input-to-state stability,
- delayed systems,
- bounded-delay impulses,
- Halanay-type inequality
Citation: Bangxin Jiang, Yijun Lou, Jianquan Lu. Input-to-state stability of delayed systems with bounded-delay impulses[J]. Mathematical Modelling and Control, 2022, 2(2): 44-54. doi: 10.3934/mmc.2022006

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Abstract

This paper considers the input-to-state stability (ISS) of delayed systems with bounded-delay impulses, where the delays in impulses are arbitrarily large but bounded. A novel Halanay-type inequality with delayed impulses and external inputs is proposed to deeply evaluate the effects of delayed impulses on ISS of delayed systems. Then, we obtain some delay-independent ISS criteria for the addressed delayed systems by using Lyapunov method. Particularly, by applying a new analysis technique, the current study enriches the Halanay-type inequalities and further improve the results derived in ^[1]. Two illustrative examples are presented to validate theoretical results.

References

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