Incremental Nonlinear Stability Analysis for Stochastic Systems Perturbed by Lévy Noise

Abstract

We present a theoretical framework for characterizing incremental stability of nonlinear stochastic systems perturbed by additive noise of two types: compound Poisson shot noise and bounded-measure Lévy noise. For each type, we show that trajectories of the system with distinct initial conditions and noise sample paths exponentially converge towards a bounded error ball of each other in the expected mean-squared sense under certain boundedness assumptions. The practical utilities of this study include the model-based design of stochastic controllers/observers that are able to handle a much broader class of noise than Gaussian white. We demonstrate our results using three case studies.