Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Input-to-state Stability in the Meaning of Switching for Delayed Feedback Switched Stochastic Financial System

Version 1 : Received: 3 September 2020 / Approved: 4 September 2020 / Online: 4 September 2020 (11:13:14 CEST)

How to cite: Rao, R. Input-to-state Stability in the Meaning of Switching for Delayed Feedback Switched Stochastic Financial System. Preprints 2020, 2020090099 (doi: 10.20944/preprints202009.0099.v1). Rao, R. Input-to-state Stability in the Meaning of Switching for Delayed Feedback Switched Stochastic Financial System. Preprints 2020, 2020090099 (doi: 10.20944/preprints202009.0099.v1).

## 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 financial crisis often erupts periodically, which illuminates that the global stability in the classical sense is actually meaningless. 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.

## Keywords

switched system; asymptotical stability; Lyapunov function; $L^p$ space; non-Lipschitz function

## Subject

MATHEMATICS & COMPUTER SCIENCE, Applied Mathematics

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