Output-feedback stabilization of stochastic nonlinear systems driven by noise of unknown covariance

We address the class of stochastic output-feedback nonlinear systems driven by noise whose covariance is time varying and bounded but the bound is not known a priori. This problem is analogous to deterministic disturbance att enuation problems. We first design a controller which guarantees that the s olutions converge (in probability) to a residual set proportional to the un known bound on the covariance. Then, for the case of a vanishing noise vect or field, we design an adaptive controller which, besides global stability in probability, guarantees regulation of the state of the plant to zero wit h probability one. (C) 2000 Elsevier Science B.V. All rights reserved.