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This study addresses the stability problem for linear continuous‐time Markovian switching singular systems. Based on a refined description for jumps of the system states at the switching instants, sufficient conditions for exponential stability in the mean‐square sense of the Markovian switching singular system are obtained by means of multiple Lyapunov function method. The obtained results present a new analysis of the impact for switching law‐induced state jump on the stability property of the considered system. Numerical examples are presented to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]