Observer design for a class of singular stochastic nonlinear systems

In this paper, we deal with observer design for a class of nonlinear stochastic singular systems with multiplicative noises. The dynamics of the considered systems is described by a stochastic differential algebraic equation (SDAE) driven by a brownian motion. The nonlinearities of the dynamics are assumed to be one-sided Lipschitz. Based on the adaptation of Itô calculus for SDAE, we derived the conditions to obtain the almost surely exponential stability of the equilibrium point of the observation error. It is shown that the almost sure exponential convergence of the observation error could be treated by decoupling the state from this error. This is done by using a new theorem dedicated to triangular stochastic systems.