Practical asymptotic stability of stochastic systems driven by Lévy processes and its application to control of TORA systems

Abstract

Two Lyapunov-type theorems are developed to investigate global (practical) asymptotic stability in probability for SDEs driven by (non-vanishing) Lévy processes, which can be either affine or non-affine or both in the states. These theorems provide sufficient conditions for the stability, which are relatively easy to be verified, and thus have a potential application in control design. The theoretical development is then applied to design feedback stabilisers for global (practical) asymptotic stability in probability for a translating oscillator with a rotating actuator (TORA) system.