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Feedback, correlations, and propagation of mean anisotropy of signals in filter connections

Alexander Kurdyukov, Igor Vladimirov
The anisotropy-based approach to robust control in stochastic systems occupies a unifying intermediate position between the $\cH_2$ and $\cH_{\infty}$-optimal
control theories. Initiated at the interface of Information Theory and Robust Control about thirteen years ago, the approach employs the $a$-anisotropic norm of a linear system as its worst-case sensitivity to input random disturbances whose mean anisotropy is bounded by a nonnegative parameter $a$. The latter quantifies the temporal ``colouredness'' and spatial ``non-roundness'' of the signal by its minimal relative entropy production rate with respect to Gaussian white noises with scalar covariance matrices. Revisiting the underlying definitions, the paper emphasizes the role of feedback in the construct of mean anisotropy of signals and discusses propagation of the latter through various filter connections. The results can be used to support physical and engineering intuition for a ``rational" choice of the mean anisotropy level $a$ in the design of anisotropy-based robust controllers.
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