Exponential stabilisation and dissipativity analysis of semilinear parabolic systems

Mathiyalagan, K.; Ragul, R.; Park, Ju H.; Palraj, Jothiappan

doi:10.1080/00207721.2020.1793228

Cited by 5 publications

(2 citation statements)

References 22 publications

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“…Mathiyalagan et al had contributed to the establishment of conditions for mean-square and almost sure exponential stability in both semi-linear stochastic partial differential systems affected by Lévy noise using linear matrix inequalities (LMIs), 33 and in linear stochastic neutral systems with general time-delays governed by Stieltjes integrals. 34 Zhang and Li 35 investigate the delay-dependent exponential stability of linear stochastic neutral systems with general delays, utilizing Stieltjes integrals to provide a unified approach in determining stability through spectral radius and linear matrix inequalities. In numerous practical systems, time delays and stochastic disturbances are inevitably introduced due to factors such as signal transmission, processing, or control.…”

Section: Introductionmentioning

confidence: 99%

“…Noteworthy studies on stochastic disturbance include the work of Xu et al, 31 who investigated spacing errors between vehicles in a longitudinal following system with stochastic disturbance, and Hu et al, 32 who applied stochastic programming to address stochastic disturbances in vehicle platoons. Mathiyalagan et al had contributed to the establishment of conditions for mean‐square and almost sure exponential stability in both semi‐linear stochastic partial differential systems affected by Lévy noise using linear matrix inequalities (LMIs), 33 and in linear stochastic neutral systems with general time‐delays governed by Stieltjes integrals 34 . Zhang and Li 35 investigate the delay‐dependent exponential stability of linear stochastic neutral systems with general delays, utilizing Stieltjes integrals to provide a unified approach in determining stability through spectral radius and linear matrix inequalities.…”

Section: Introductionmentioning

confidence: 99%

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Exponential mean‐square string stability of vehicular platoon with stochastic disturbance and time delay

Sui,

Zhang,

Dai

2024

Intl J Robust & Nonlinear

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Platooning is an effective way to reduce air resistance and fuel consumption in vehicular transportation. However, stochastically generated disturbances can significantly impact the string stability of platoons. This article proposes a novel control law, based on sliding mode control and leader‐predecessor communications, designed to improve the exponential mean‐square string stability of platoons with Ito‐type stochastic disturbances that consider friction force. Specifically, our approach employs a third‐order nonlinear dynamic model to capture the relevant spatiotemporal correlations present in vehicle platoons. The proposed longitudinal control strategy effectively stabilizes the platoons with time delay and was verified through simulation experimentation. In this study, the stability of sliding mode motion is thoroughly investigated by means of sub‐reachable and practical stability analysis with sliding mode control. The findings of this study provide a theoretical foundation for further research on vehicle platoons with increasingly complicated interference and time delays. Overall, our results demonstrate that our approach can achieve significant improvements in both fuel economy and exhaust emissions while maintaining high levels of string stability, further contributing to the development of efficient and sustainable transportation systems.

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Section: Introductionmentioning

confidence: 99%