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Abstract: This paper deals with the observer design problem for a class of descriptor Markovian jumping systems with nonlinear perturbations. The problem addressed is to design full-order and reduced-order observers, respectively, such that the dynamics of each estimation error is guaranteed to be globally exponentially stable in the mean square. Sufficient conditions for the existence of both full-order and reduced-order observers are given, which are equivalent to a set of linear matrix inequalities. An example is presented to illustrate the effectiveness of the proposed method.