V.A. Boichenko. Anisotropy and spectral entropy: Axiomatic approach ... P. 53-65

Real-life dynamic systems operate under various disturbances and are affected by unknown external influences. That is why the problem of perturbation suppression is an extremely important branch of control theory. An effective approach to solving this problem is the anisotropic theory of stochastic robust control. Unfortunately, this theory has fundamental limitations — it is applicable only to discrete stochastic systems and only to stationary Gaussian sequences. Recently, attempts have been made to transfer the concepts of anisotropic theory to systems with continuous time. In this paper, the results of anisotropic theory are extended to arbitrary random signals, including both sequences with finite $l_2$ or power norm and sequences with arbitrary growth rate.

Keywords: linear systems, anisotropy, spectral entropy, $\sigma$-entropy norm

Received June 1, 2022

Revised June 17, 2022

Accepted June 20, 2022

Victor Aleksandrovich Boichenko, Cand. Sci. (Phys.-Math.), V.A.Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, 117997 Russia, e-mail: v.boichenko@gmail.com


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Cite this article as: V.A. Boichenko. Anisotropy and spectral entropy: Axiomatic approach. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2022, vol. 28, no. 3, pp. 53–65.