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This paper considers a disturbance attenuation problem for a linear discretetime invariant system under random disturbances with imprecisely knownprobability distributions. The statistical uncertainty is measured in terms ofrelative entropy using the mean anisotropy functional. The disturbanceattenuation capabilities of the system are quantified by the anisotropic normwhich is a stochastic counterpart of the H-infinity norm. The designedanisotropic suboptimal controller generally is a dynamic fixed-orderoutput-feedback compensator which is required to stabilize the closed-loopsystem and keep its anisotropic norm below a prescribed threshold value.

Synthesis of anisotropic suboptimal controllers by convex optimization