Input-to-state stability in the meaning of switching for delayed feedback switched stochastic financial system

Ruofeng Rao; Xiaodi Li; Ruofeng Rao; Xiaodi Li

doi:10.3934/math.2021062

AIMS Mathematics

2021, Volume 6, Issue 1: 1040-1064. doi: 10.3934/math.2021062

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Research article

Input-to-state stability in the meaning of switching for delayed feedback switched stochastic financial system

Ruofeng Rao ^{1,2
,
,},
Xiaodi Li ^3,†

1.
School of Mathematical Sciences, Sichuan Normal University, Chengdu, 610066, China
2.
Department of Mathematics, Chengdu Normal University, Chengdu, 611130, China
3.
School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China
† Contributed equally as the first author

Received: 30 August 2020 Accepted: 03 November 2020 Published: 06 November 2020
MSC : 34D23, 93D05

Financial system is essentially chaotic and unstable if there is not any external inputs. By means of Lyapunov function method, design of switching law, novel fuzzy assumption, $L^p$ estimation technique and Laplace semigroup theory, the author presents the boundedness and LMI-based (globally) asymptotical input-to-state stability criteria of financial systems. Particularly, the globally asymptotical stability in the meaning of switching implies that when the time $t$ is big enough, the dynamic of any subsystem must approach its unique equilibrium point. Besides, the global stability in the classical sense is not applicable to eruption of the periodical financial crisis. So the stability in the meaning of switching proposed in this paper is suitable and appropriate. Numerical examples illuminate the effectiveness of the obtained results.
- switched system,
- Lyapunov function,
- $L^p$ space,
- non-Lipschitz function
Citation: Ruofeng Rao, Xiaodi Li. Input-to-state stability in the meaning of switching for delayed feedback switched stochastic financial system[J]. AIMS Mathematics, 2021, 6(1): 1040-1064. doi: 10.3934/math.2021062

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Abstract

Financial system is essentially chaotic and unstable if there is not any external inputs. By means of Lyapunov function method, design of switching law, novel fuzzy assumption, $L^p$ estimation technique and Laplace semigroup theory, the author presents the boundedness and LMI-based (globally) asymptotical input-to-state stability criteria of financial systems. Particularly, the globally asymptotical stability in the meaning of switching implies that when the time $t$ is big enough, the dynamic of any subsystem must approach its unique equilibrium point. Besides, the global stability in the classical sense is not applicable to eruption of the periodical financial crisis. So the stability in the meaning of switching proposed in this paper is suitable and appropriate. Numerical examples illuminate the effectiveness of the obtained results.

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