Abstract: This paper concerns the design problem of state feedback robust variance controllers which guarantee the closed-loop poles in a specified disk and steady-state variance to be less than a given upper bound for linear systems with linear fractional parameter uncertainties. Conditions for existence of such controllers are derived and it is shown that this condition is equivalent to the solvability of a certain linear matrix inequality (LMI) system. A parameterized representation of a set of desired controllers is characterized in terms of the feasible solutions to the LMI system. Based on this, the solution to a minimum-energy variance controller design problem is presented.