Improved accumulative-error event-triggered control for discrete-time linear systems with random time delays

Zhi Fu; Shen-Ping Xiao; Jiang-Lin Huang; Chang-Xin Li; Zhi Fu; Shen-Ping Xiao; Jiang-Lin Huang; Chang-Xin Li

doi:10.3934/math.20251004

AIMS Mathematics

2025, Volume 10, Issue 9: 22561-22578. doi: 10.3934/math.20251004

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Research article

Improved accumulative-error event-triggered control for discrete-time linear systems with random time delays

1.
College of Transportations and Electrical Engineering Hunan University of Technology, Zhuzhou412007, China
2.
Changsha University of Science and Engineering, School of Intelligent Transportation and Vehicle Engineering, Changsha41000, China
3.
Key Laboratory for Electric Drive Control and Intelligent Equipment of Hunan Province, Zhuzhou412007, China

Received: 02 July 2025 Revised: 21 September 2025 Accepted: 25 September 2025 Published: 29 September 2025
MSC : 34D20, 60J20, 93D30, 93B40

A stability problem under event-triggered control for discrete linear systems with random time delays is considered in this paper. First, this paper improves an accumulative error-based event-triggered approach, which can switch the event-triggered parameter between the two-modes over time. Second, a new closed-loop discrete Markov switching system equation is derived by decoupling the accumulative error term, and the time delays are equal to the current Markov modes when the event-triggered scheme is met. Third, the co-designing problems for control gains and event-triggered parameters in the system are solved. Finally, the stochastic stability of the system is guaranteed through random analysis techniques and a free-weighting matrix method, and the effectiveness of the approach is demonstrated by using numerical examples.
- discrete-time linear systems,
- event-triggered control,
- Markov chain,
- free-weight matrix method,
- co-designing control
Citation: Zhi Fu, Shen-Ping Xiao, Jiang-Lin Huang, Chang-Xin Li. Improved accumulative-error event-triggered control for discrete-time linear systems with random time delays[J]. AIMS Mathematics, 2025, 10(9): 22561-22578. doi: 10.3934/math.20251004

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Abstract

A stability problem under event-triggered control for discrete linear systems with random time delays is considered in this paper. First, this paper improves an accumulative error-based event-triggered approach, which can switch the event-triggered parameter between the two-modes over time. Second, a new closed-loop discrete Markov switching system equation is derived by decoupling the accumulative error term, and the time delays are equal to the current Markov modes when the event-triggered scheme is met. Third, the co-designing problems for control gains and event-triggered parameters in the system are solved. Finally, the stochastic stability of the system is guaranteed through random analysis techniques and a free-weighting matrix method, and the effectiveness of the approach is demonstrated by using numerical examples.

References

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