Robust finite-time stability of nonlinear systems involving hybrid impulses with application to sliding-mode control

Jian Meng; Bin Zhang; Tengda Wei; Xinyi He; Xiaodi Li; Jian Meng; Bin Zhang; Tengda Wei; Xinyi He; Xiaodi Li

doi:10.3934/mbe.2023196

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 2: 4198-4218. doi: 10.3934/mbe.2023196

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Robust finite-time stability of nonlinear systems involving hybrid impulses with application to sliding-mode control

1.
State Grid Intelligence Technology Co., Ltd, Jinan 250000, China
2.
School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
Academic editor: Shengqiang Liu

Received: 17 October 2022 Revised: 30 November 2022 Accepted: 14 December 2022 Published: 21 December 2022

This paper is concerned with the robust finite-time stability and stabilization of impulsive systems subject to hybrid disturbances that consists of external disturbances and hybrid impulses with time-varying jump maps. First, the global finite-time stability and local finite-time stability of a scalar impulsive system are ensured by the analysis of cumulative effect of hybrid impulses. Then, asymptotic stabilization and finite-time stabilization of second-order system subject to hybrid disturbances are achieved by linear sliding-mode control and non-singular terminal sliding-mode control. It shows that the stable systems under control are robust to external disturbances and hybrid impulses with non-destabilizing cumulative effect. If the hybrid impulses have destabilizing cumulative effect, the systems are also capable of absorbing the hybrid impulsive disturbances by the designed sliding-mode control strategies. Finally, the effectiveness of theoretical results is verified by numerical simulation and the tracking control of linear motor.
- robust finite-time stability,
- hybrid impulse,
- sliding-mode control,
- second-order dynamics
Citation: Jian Meng, Bin Zhang, Tengda Wei, Xinyi He, Xiaodi Li. Robust finite-time stability of nonlinear systems involving hybrid impulses with application to sliding-mode control[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 4198-4218. doi: 10.3934/mbe.2023196

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Abstract

This paper is concerned with the robust finite-time stability and stabilization of impulsive systems subject to hybrid disturbances that consists of external disturbances and hybrid impulses with time-varying jump maps. First, the global finite-time stability and local finite-time stability of a scalar impulsive system are ensured by the analysis of cumulative effect of hybrid impulses. Then, asymptotic stabilization and finite-time stabilization of second-order system subject to hybrid disturbances are achieved by linear sliding-mode control and non-singular terminal sliding-mode control. It shows that the stable systems under control are robust to external disturbances and hybrid impulses with non-destabilizing cumulative effect. If the hybrid impulses have destabilizing cumulative effect, the systems are also capable of absorbing the hybrid impulsive disturbances by the designed sliding-mode control strategies. Finally, the effectiveness of theoretical results is verified by numerical simulation and the tracking control of linear motor.

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