Input-to-state stability of nonlinear systems with delayed impulse based on event-triggered impulse control

Linni Li; Jin-E Zhang; Linni Li; Jin-E Zhang

doi:10.3934/math.20241287

AIMS Mathematics

2024, Volume 9, Issue 10: 26446-26461. doi: 10.3934/math.20241287

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Input-to-state stability of nonlinear systems with delayed impulse based on event-triggered impulse control

Linni Li ,
Jin-E Zhang ^,

School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China

Received: 26 July 2024 Revised: 30 August 2024 Accepted: 06 September 2024 Published: 12 September 2024
MSC : 93C30

This paper investigates input-to-state stability (ISS) of nonlinear systems with delayed impulse under event-triggered impulse control, where external inputs are different in continuous and impulse dynamics. First, an event-triggered mechanism (ETM) is proposed to avoid Zeno behavior. In order to ensure ISS of the considered system, the relationship among event triggering parameters, impulse intensity, and impulse delay is constructed. Then, as an application, ETM and impulse control gain for a specific kind of nonlinear systems are presented based on linear matrix inequalities (LMI). Finally, two examples confirm the feasibility and usefulness of the proposed strategy.
- input-to-state stability,
- nonlinear delayed impulse,
- event-triggered impulse control,
- nonlinear systems,
- Zeno behavior
Citation: Linni Li, Jin-E Zhang. Input-to-state stability of nonlinear systems with delayed impulse based on event-triggered impulse control[J]. AIMS Mathematics, 2024, 9(10): 26446-26461. doi: 10.3934/math.20241287

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Abstract

This paper investigates input-to-state stability (ISS) of nonlinear systems with delayed impulse under event-triggered impulse control, where external inputs are different in continuous and impulse dynamics. First, an event-triggered mechanism (ETM) is proposed to avoid Zeno behavior. In order to ensure ISS of the considered system, the relationship among event triggering parameters, impulse intensity, and impulse delay is constructed. Then, as an application, ETM and impulse control gain for a specific kind of nonlinear systems are presented based on linear matrix inequalities (LMI). Finally, two examples confirm the feasibility and usefulness of the proposed strategy.

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