Exponentially convergent robust and adaptive observers for uncertain stochastic systems

We present mean square exponentially convergent state observers for nonlinear stochastic systems driven by Wiener noise. The method is based on extension of variable structure observer schemes using exponential nonlinear gain. The adaptive version of the results are provided to be used when the matching uncertainty has unknown bounds. It is also shown how these results can be applied to system and measurement equations having colored noise processes.