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This paper is concerned with the mean square exponential stability and stabilization problems of Markovian jump systems with time delay. New Lyapunov functionals are proposed by choosing distinct Lyapunov matrices for different system modes and introducing a triple-integral term. Some delay-dependent conditions, including some existing results as their special cases, are derived under which the resulting closed-loop system is mean square exponentially stable with a decay rate. The design of the feedback gain matrices is accomplished by solving linear matrix inequalities. Finally, the effectiveness and performance of the obtained results are demonstrated by numerical examples.