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This paper is concerned with robust performance criteria for linearcontinuous time invariant stochastic systems driven by statistically uncertainrandom processes. The uncertainty is understood as the deviation of impreciselyknown probability distributions of the input disturbance from those of thestandard Wiener process. Using a one-parameter family of conformal maps of theunit disk in the complex plane onto the right half-plane for discrete andcontinuous time transfer functions, the deviation from the nominal Gaussianwhite-noise model is quantified by the mean anisotropy for the input of adiscrete-time counterpart of the original system. The parameter of thisconformal correspondence specifies the time scale for filtered versions of theinput and output of the system, in terms of which the worst-case root meansquare gain is formulated subject to an upper constraint on the meananisotropy. The resulting two-parameter counterpart of theanisotropy-constrained norm of the system for the continuous time case isamenable to state-space computation using the methods of the anisotropy-basedtheory of stochastic robust filtering and control, originated by the author inthe mid 1990s.

Anisotropy-based robust performance criteria for statistically uncertain linear continuous time invariant stochastic systems