Almost sure exponential stability of dynamical systems driven by Lévy processes and its application to control design for magnetic bearings

A Lyapunov-type theorem is developed to study well-posedness and almost surely (Formula presented.)-exponential stability of dynamical systems driven by Lévy processes. Sufficient conditions imposed by the theorem, which are relatively easy to be verified, make it applicable to control design and stability analysis. The theorem is then applied to design tracking controllers to achieve almost surely (Formula presented.)-exponential stability for magnetic bearings under diffuse-jump loads subject to an output tracking constraint