This technical note is concerned with exploring a new approach for the analysis and synthesis for Markov jump linear systems with incomplete transition descriptions. In the study, not all the elements of the transition rate matrices (TRMs) in continuous-time domain, or transition probability matrices (TPMs) in discrete-time domain are assumed to be known. By fully considering the properties of the TRMs and TPMs, and the convexity of the uncertain domains, necessary and sufficient criteria of stability and stabilization are obtained in both continuous and discrete time. Numerical examples are used to illustrate the results.