Backstepping control design for stochastic systems driven by Lévy processes

Abstract

This paper presents a constructive method to design control inputs that almost surely globally ${\mathcal{K}}_{\mathrm{\infty }}$-exponentially stabilise strict-feedback systems driven by Lévy processes, which consist of Wiener and compensated Poisson processes, at the origin. The control design is based on a recently developed Lyapunov-type theorem for the study of well-posedness and almost sure ${\mathcal{K}}_{\mathrm{\infty }}$-exponential stability of SDEs driven by Lévy processes, the backstepping method, and new Lyapunov functions.

Keywords:

• Strict feedback systems
• Lyapunov-type theorem
• well-posedness
• almost sure stability
• Lévy processes

Disclosure statement

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

Additional information

Funding

This work was supported in part by the Australian Research Council (ARC) under grant number: DP190103279.