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Most engineering systems have multiple performance objectives. Often these objectives are expressed explicitly in terms of the root-mena-squared (rms) values of the closed loop system states or outputs. This paper introduces a theory for designing linear state feedback controllers to directly accommodate these rms design constraints. The design procedure is multiobjective but requires only linear computations. Additionally, a measure of system robustness is offered. This measure is used to define a set of allowable perturbations to the system matrices such that the rms design objectives are still satisfied. A design example is included.