Incremental nonlinear stability analysis of stochastic systems perturbed by Lévy noise

We present a theoretical framework for characterizing incremental stability of nonlinear stochastic systems perturbed by either compound Poisson shot noise or finite-measure Lévy noise. For each type, we compare trajectories the system with distinct sample paths against nominal, unperturbed system. show that finite number jumps arising from process, mean-squared error between exponentially converge toward bounded ball across interval time under practical boundedness assumptions. The convergence rate is same as stable nominal system, but tradeoff parameters process and size ball. are shown to be nearly direct sums respective quantities white separately, result which analogous Lévy–Khintchine theorem. demonstrate both empirical analytical computation using several numerical examples, illustrate how varying affect tightness bound.