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.

中文翻译：

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Lévy过程驱动的随机系统的反步控制设计

本文提出了一种设计控制输入的建设性方法，该方法几乎可以肯定地全局 ${\mathcal{钾}}_{\mathrm{\infty }}$- 指数稳定由 Lévy 过程驱动的严格反馈系统，该系统由维纳过程和补偿泊松过程组成，在原点。控制设计基于最近开发的李雅普诺夫型定理，用于研究适定性和几乎肯定${\mathcal{钾}}_{\mathrm{\infty }}$-由 Lévy 过程、backstepping 方法和新的 Lyapunov 函数驱动的 SDE 的指数稳定性。