Local stabilization for a hyperchaotic finance system via time-delayed feedback based on discrete-time observations

Erfeng Xu; Wenxing Xiao; Yonggang Chen; Erfeng Xu; Wenxing Xiao; Yonggang Chen

doi:10.3934/math.20231045

AIMS Mathematics

2023, Volume 8, Issue 9: 20510-20529. doi: 10.3934/math.20231045

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Research article

Local stabilization for a hyperchaotic finance system via time-delayed feedback based on discrete-time observations

1.
Department of Tourism Management, Henan Institute of Science and Technology, Xinxiang 453003, China
2.
School of Economics and Management, Henan Institute of Science and Technology, Xinxiang 453003, China
3.
School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China

Received: 18 March 2023 Revised: 13 June 2023 Accepted: 19 June 2023 Published: 25 June 2023
MSC : 93C10, 93C43

This paper considers the local stabilization problem for a hyperchaotic finance system by using a time-delayed feedback controller based on discrete-time observations. The quadratic system theory is employed to represent the nonlinear finance system and a piecewise augmented discontinuous Lyapunov-Krasovskii functional is constructed to analyze the stability of the closed-loop system. By further incorporating some advanced integral inequalities, a stabilization criterion is proposed by means of the feasibility of a set of linear matrix inequalities under which the hyperchaotic finance system can be asymptotically stabilized for any initial condition satisfying certain constraint. As the by-product, a simplified criterion is also obtained for the case without time delay. Moreover, the optimization problems with respect to the domain of attraction are specially discussed, which are transformed into the minimization problems subject to linear matrix inequalities. Finally, numerical simulations are provided to illustrate the effectiveness of the derived results.
- local stabilization,
- hyperchaotic finance system,
- time-delayed feedback,
- discrete-time observations
Citation: Erfeng Xu, Wenxing Xiao, Yonggang Chen. Local stabilization for a hyperchaotic finance system via time-delayed feedback based on discrete-time observations[J]. AIMS Mathematics, 2023, 8(9): 20510-20529. doi: 10.3934/math.20231045

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Abstract

This paper considers the local stabilization problem for a hyperchaotic finance system by using a time-delayed feedback controller based on discrete-time observations. The quadratic system theory is employed to represent the nonlinear finance system and a piecewise augmented discontinuous Lyapunov-Krasovskii functional is constructed to analyze the stability of the closed-loop system. By further incorporating some advanced integral inequalities, a stabilization criterion is proposed by means of the feasibility of a set of linear matrix inequalities under which the hyperchaotic finance system can be asymptotically stabilized for any initial condition satisfying certain constraint. As the by-product, a simplified criterion is also obtained for the case without time delay. Moreover, the optimization problems with respect to the domain of attraction are specially discussed, which are transformed into the minimization problems subject to linear matrix inequalities. Finally, numerical simulations are provided to illustrate the effectiveness of the derived results.

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