Stability of SDRE observers is usually analyzed in a deterministic framework, where the performance of the observer is not perturbed by external noises. However, plant uncertainty and measurement noises are not negligible in real implementations. In this paper based on the stability results developed for Kalman-Bucy filters and stochastic stability analysis of nonlinear systems, the stability of an SDRE filter is analyzed in discrete-time domain. Sufficient conditions are given to limit the estimation errors in sense of mean-squared measure. Furthermore, it is shown that in practical situations there exist feasible regions to satisfy the stability conditions, provided that the initial error and the norm of plant uncertainty and measurement noises are sufficiently small. Finally, the stability conditions are verified through simulation of a typical nonlinear system.

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