A new decomposition method for stochastic dynamic stabilization

The aim of this paper is to prove that the stabilizability of a controlled nonlinear stochastic system can be deduced from the stabilizability of a “reduced” system for which the existence of a stabilizing feedback law can be decided more easily. This result extends the well-known deterministic “chain of integrator lemma” by using a different scheme of reduction for the original stochastic system.