Abstract: The positive real analysis and synthesis problems are investigated for a class of linear systems with random jump parameters. The dynamics of the jump parameters is modeled by a continuous-time finite-state Markov process. Based on stochastic Lyapunov functional approach, both state and output-feedback mode-dependent controllers are proposed to guarantee the strict positive realness of the resulting closed-loop systems. For the Markov jump systems subject to parametric uncertainties, sufficient conditions which are in terms of solutions of a set of coupled linear matrix inequalities are developed to design robust controllers such that stochastic stability and positive realness property hold irrespective of all admissible uncertainties.