Abstract: The design of a state feedback robust variance controller is considered, which guarantees the closed-loop steady-state variance to be less than a given upper bound and concerns some H∞ performance for a class of Markov jump systems whose mode is not available completely. Based on linear matrix inequality (LMI) method, system variance is analyzed and the existence conditions of such controllers are proposed and proved. A parameterized representation of a set of desired controllers is characterized in terms of the feasible solutions to the LMI system. The problem of designing the minimum variance robust controller is formulated as a convex problem with LMI constrains. Finally, the simulation results show the effectiveness of the method proposed in this paper.