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In this study, the stability analysis and synthesis problems for continuous Markov jump linear systems with partly known transition probabilities are investigated. The partly known transition probabilities cover the cases that some elements are known, some are unknown with known lower and upper bounds and some are completely unknown. By making full use of the continuous transition probability matrix property, that is, the sum of transition probabilities is 0 for each row, a new method for the analysis and synthesis is presented in terms of solvability of a set of linear matrix inequalities. Compared to the existing results in the literature, it is shown that the proposed method is more effective to deal with the considered transition probabilities. Numerical examples are given to show the validity of the proposed method.