State feedback stabilization problem of stochastic high-order and low-order nonlinear systems with time-delay

Yanghe Cao; Junsheng Zhao; Zongyao Sun; Yanghe Cao; Junsheng Zhao; Zongyao Sun

doi:10.3934/math.2023163

AIMS Mathematics

2023, Volume 8, Issue 2: 3185-3203. doi: 10.3934/math.2023163

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Research article

State feedback stabilization problem of stochastic high-order and low-order nonlinear systems with time-delay

1.
School of Mathematical Science, Liaocheng University, Liaocheng 252059, China
2.
Institute of Automation, Qufu Normal University, Qufu 273100, China

Received: 17 September 2022 Revised: 18 October 2022 Accepted: 26 October 2022 Published: 16 November 2022
MSC : 93D12, 93B52, 93E15

This manuscript considers the state feedback stabilization problem for a class of stochastic high-order and low-order nonlinear systems with time-delay. Compared with the previous results, a distinctive feature to be studied is that the considered systems involve high-order, low-order, intricate stochastic diffusion terms and time-delay simultaneously. First, the homogeneous domination approach and suitable coordinate transformations are introduced to obtain the updating laws. Then, a state feedback controller is devised to make the closed-loop systems globally asymptotically stable in probability. Finally, a simulation example is shown to prove the proposed approach powerfully.
- homogeneous domination approach,
- high-order and low-order,
- state feedback,
- stochastic nonlinear systems with time-delay
Citation: Yanghe Cao, Junsheng Zhao, Zongyao Sun. State feedback stabilization problem of stochastic high-order and low-order nonlinear systems with time-delay[J]. AIMS Mathematics, 2023, 8(2): 3185-3203. doi: 10.3934/math.2023163

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Abstract

This manuscript considers the state feedback stabilization problem for a class of stochastic high-order and low-order nonlinear systems with time-delay. Compared with the previous results, a distinctive feature to be studied is that the considered systems involve high-order, low-order, intricate stochastic diffusion terms and time-delay simultaneously. First, the homogeneous domination approach and suitable coordinate transformations are introduced to obtain the updating laws. Then, a state feedback controller is devised to make the closed-loop systems globally asymptotically stable in probability. Finally, a simulation example is shown to prove the proposed approach powerfully.

References

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