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Volume 10
Issue 19
10.3390/electronics10192346
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Article

Study on the Lyapunov Stability of a Time-Discrete Macro Traffic System with Variable Delay and Feedback Control

by
Shan Jiang
1,
Geng Zhang
1,*,
Yu Zhang
1,
Dong-Bo Pan
2 and
Wen-Ze Xiong
3
1
College of Computer and Information Science, Southwest University, Chongqing 400715, China
2
College of Artificial Intelligence, Southwest University, Chongqing 400715, China
3
Instrumentation Technology and Economy Institute (ITEI), Beijing 100055, China
*
Author to whom correspondence should be addressed.
Electronics 2021, 10(19), 2346; https://doi.org/10.3390/electronics10192346
Submission received: 26 August 2021 / Revised: 20 September 2021 / Accepted: 22 September 2021 / Published: 25 September 2021
(This article belongs to the Section Industrial Electronics)
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Abstract

This paper constructs and analyzes a time-discrete macro traffic system with bounded variable delay and feedback control strategy. By theoretical analysis using the Lyapunov theorem, a stable condition of the macro traffic system is derived under which traffic jams can be suppressed. The traffic developing properties of the new traffic system for different variable delay and feedback control parameters are illustrated through simulation. The results show that variable delay can easily lead a traffic system to evolve into a traffic jam, and the feedback control strategy can enhance the stability of the traffic system with respect to variable delay. Moreover, the traffic unstable level caused by variable delay is less than the unstable extent caused by the constant upper bound of variable delay; still it is more serious than the traffic fluctuation caused by the constant lower bound of variable delay.
Keywords: time-discrete lattice hydrodynamic model; variable delay; Lyapunov function time-discrete lattice hydrodynamic model; variable delay; Lyapunov function

Share and Cite

MDPI and ACS Style

Jiang, S.; Zhang, G.; Zhang, Y.; Pan, D.-B.; Xiong, W.-Z. Study on the Lyapunov Stability of a Time-Discrete Macro Traffic System with Variable Delay and Feedback Control. Electronics 2021, 10, 2346. https://doi.org/10.3390/electronics10192346

AMA Style

Jiang S, Zhang G, Zhang Y, Pan D-B, Xiong W-Z. Study on the Lyapunov Stability of a Time-Discrete Macro Traffic System with Variable Delay and Feedback Control. Electronics. 2021; 10(19):2346. https://doi.org/10.3390/electronics10192346

Chicago/Turabian Style

Jiang, Shan, Geng Zhang, Yu Zhang, Dong-Bo Pan, and Wen-Ze Xiong. 2021. "Study on the Lyapunov Stability of a Time-Discrete Macro Traffic System with Variable Delay and Feedback Control" Electronics 10, no. 19: 2346. https://doi.org/10.3390/electronics10192346

APA Style

Jiang, S., Zhang, G., Zhang, Y., Pan, D.-B., & Xiong, W.-Z. (2021). Study on the Lyapunov Stability of a Time-Discrete Macro Traffic System with Variable Delay and Feedback Control. Electronics, 10(19), 2346. https://doi.org/10.3390/electronics10192346

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