Intermittent control for stabilization of uncertain nonlinear systems via event-triggered mechanism

Tian Xu; Jin-E Zhang; Tian Xu; Jin-E Zhang

doi:10.3934/math.20241382

AIMS Mathematics

2024, Volume 9, Issue 10: 28487-28507. doi: 10.3934/math.20241382

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Intermittent control for stabilization of uncertain nonlinear systems via event-triggered mechanism

Tian Xu ,
Jin-E Zhang ^,

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

Received: 26 July 2024 Revised: 12 September 2024 Accepted: 26 September 2024 Published: 08 October 2024
MSC : 93C10, 93D15

This paper studies the finite-time stabilization (FTS) and finite-time contraction stabilization (FTCS) of parameter-uncertain systems subjected to impulsive disturbances by using an event-triggered aperiodic intermittent control (EAPIC) method, which combines aperiodic intermittent control with event-triggered control. By employing the Lyapunov method and linear matrix inequality techniques, sufficient conditions for FTS and FTCS are derived. Additionally, within the finite-time control framework, relationships among impulsive disturbance, intermittent control parameters, and event-triggered mechanism (ETM) thresholds are established under EAPIC to ensure FTS and FTCS. The sequence of impulsive moments is determined by a predetermined ETM, and Zeno phenomena are also excluded. Finally, the effectiveness of the EAPIC approach is demonstrated through two numerical examples.
- finite-time,
- uncertain nonlinear systems,
- impulsive disturbance,
- aperiodic intermittent control
Citation: Tian Xu, Jin-E Zhang. Intermittent control for stabilization of uncertain nonlinear systems via event-triggered mechanism[J]. AIMS Mathematics, 2024, 9(10): 28487-28507. doi: 10.3934/math.20241382

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Abstract

This paper studies the finite-time stabilization (FTS) and finite-time contraction stabilization (FTCS) of parameter-uncertain systems subjected to impulsive disturbances by using an event-triggered aperiodic intermittent control (EAPIC) method, which combines aperiodic intermittent control with event-triggered control. By employing the Lyapunov method and linear matrix inequality techniques, sufficient conditions for FTS and FTCS are derived. Additionally, within the finite-time control framework, relationships among impulsive disturbance, intermittent control parameters, and event-triggered mechanism (ETM) thresholds are established under EAPIC to ensure FTS and FTCS. The sequence of impulsive moments is determined by a predetermined ETM, and Zeno phenomena are also excluded. Finally, the effectiveness of the EAPIC approach is demonstrated through two numerical examples.

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