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This paper focuses on the stability analysis and controller synthesis of continuous-time Markovian jump time-delay systems with incomplete transition rate descriptions. A general stability criterion is formulated first for state- and input-delay Markovian jump time-delay systems with fully known transition rates. On the basis of the proposed condition, an equivalent condition is given under the assumption of partly known/unknown transition rates. A new design technique based on a projection inequality has been applied to design both state feedback and static output feedback controllers. All conditions can be readily verified by efficient algorithms. Finally, illustrative examples are provided to show the effectiveness of the proposed approach.