Stochastic stabilization of nonlinear systems in feedforward form with noisy outputs

We study the problem of globally stabilizing through measurement feedback a class of uncertain stochastic nonlinear systems in feedforward (or upper triangular) form, with state equations affected by a Wiener process adapted to a given filtration of sigma-algebras and measurements affected by a sample continuous and strongly Markov stochastic process adapted to the same filtration of sigma-algebras. We propose a step-by step design, based on splitting the system F, into one-dimensional interconnected systems Sigma(j), j = 1, ..., n. Moreover, we introduce the notion of practical stability in probability, which corresponds to having a large probability of being the state small in norm whenever the noise affecting the measurements has a "small" second order moment.