Robust observer design for a class of stochastic nonlinear systems

This contribution deals with the robust observer design of some nonlinear stochastic systems with multiplicative noises. The drift part of the considered systems contain a linear part, a bilinear one and a Lipschitz nonlinearity. The uncertainties that affect the system concern all the matrices of the dynamics of this one. The parametric uncertainties under consideration are unstructured and norm-bouded. The observer design is formulated in terms of LMI to be satisfied in order to obtain the observer gains. Our approach ensures the almost sure exponential stability of the estimation error which is less conservative than the usual mean-square exponential stability.