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The design of a regulator for a system with random discontinuities in its linear perturbation model is considered. The perturbation model is assumed to have a wide-band transfer function, rather than a more conventional low-pass transfer function. The resulting design equations are more complicated than are their counterparts derived under the low-pass hypothesis. Approximations are discussed which can be used to reduce the computational burden in some cases. The analytical procedures are illustrated in an example which considers the synthesis of a steam temperature regulator for a solar-powered central receiver.