Explicit criteria for moment exponential stability and instability of switching diffusions with Lévy noise

Abstract

This paper is devoted to moment exponential stability of a class of Markovian switching diffusions with Lévy noise. Our objective is to find verifiable conditions for moment exponential stability and instability. By employing the ireducibility of the Markovian switching process and the Fredholm alternative, we derive explicit criteria for moment exponential stability and instability for linear and general nonlinear systems. Explicit contribution of the Markovian switching to the stability and instability is revealed. Using the criteria developed, we can design feedback controls or perturbations to stabilise a given diffusion with Markovian switching and Lévy noise. Several examples are provided to demonstrate our findings.

Keywords:

• Markovian switching
• jump diffusions
• moment exponential stability
• stabilisation
• Lévy noise

Acknowledgments

The authors thank the anonymous reviewer for the careful reading of the manuscript and the suggestions leading to much improvement.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Research Foundation of Korea grant funded by the Korea Government (MIST) [grant number NRF-2021R1F1A1062361].