Backstepping-based delayed impulsive control for input-to-state stabilization of disturbed electrohydraulic servo systems

Mingzhong Li; Yongming She; Wei Wang; Shuai Liu; Mingzhong Li; Yongming She; Wei Wang; Shuai Liu

doi:10.3934/math.2026857

AIMS Mathematics

2026, Volume 11, Issue 7: 21113-21127. doi: 10.3934/math.2026857

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Backstepping-based delayed impulsive control for input-to-state stabilization of disturbed electrohydraulic servo systems

1.
China Coal Research Institute, Beijing, China
2.
Beijing Tianma Intelligent Control Technology Co., Ltd., Beijing, China
3.
CHN Energy Shendong Coal Group Co., Ltd., Ordos, Inner Mongolia, China

Received: 03 April 2026 Revised: 12 June 2026 Accepted: 26 June 2026 Published: 16 July 2026
MSC : 93C10, 93C27

This paper investigates the input-to-state stability (ISS) of disturbed electrohydraulic servo systems (EHSSes) via a novel backstepping-based delayed impulsive correction control scheme, where the time delay in impulsive actions is fully considered and rigorously proven to facilitate system stabilization. First, a third-order nonlinear model of EHSS is established with explicit consideration of external disturbances. Then, a recursive backstepping method is developed to derive virtual control laws for the position velocity subsystem, rendering it ISS with respect to the acceleration error. Furthermore, by employing Lyapunov stability theory, impulsive delay inequalities, and ISS lemmas, sufficient conditions are derived to guarantee the ISS of the closed-loop error system, where the stabilizing contribution of delays involved in impulses is quantitatively analyzed within the established sufficient criteria. Finally, numerical simulations are conducted to validate that the proposed control strategy.
- impulsive control,
- input-to-state stability,
- electrohydraulic servo systems,
- backstepping-based control,
- time-delay
Citation: Mingzhong Li, Yongming She, Wei Wang, Shuai Liu. Backstepping-based delayed impulsive control for input-to-state stabilization of disturbed electrohydraulic servo systems[J]. AIMS Mathematics, 2026, 11(7): 21113-21127. doi: 10.3934/math.2026857

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Abstract

This paper investigates the input-to-state stability (ISS) of disturbed electrohydraulic servo systems (EHSSes) via a novel backstepping-based delayed impulsive correction control scheme, where the time delay in impulsive actions is fully considered and rigorously proven to facilitate system stabilization. First, a third-order nonlinear model of EHSS is established with explicit consideration of external disturbances. Then, a recursive backstepping method is developed to derive virtual control laws for the position velocity subsystem, rendering it ISS with respect to the acceleration error. Furthermore, by employing Lyapunov stability theory, impulsive delay inequalities, and ISS lemmas, sufficient conditions are derived to guarantee the ISS of the closed-loop error system, where the stabilizing contribution of delays involved in impulses is quantitatively analyzed within the established sufficient criteria. Finally, numerical simulations are conducted to validate that the proposed control strategy.

References

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