Homotopy Method for Solving Anisotropy-Based Stochastic H∞-Optimization Problem With Uncertainty

Axiomatic Foundations of Anisotropy-Based and Spectral Entropy Analysis: A Comparative Study

“…As the function S(q) is analytic, strictly increasing, and convex [10,25] on the halfinterval 0, F −2 ∞ , Equation ( 25) has a unique solution q s = S −1 (s).…”

“…Transform (21) and ( 22 make sure that the variable q parametrizes both σ-entropy gain Θ(q) of isoentropy classes K q , and σ-entropy s q of classes K q , and the set of isoentropy classes itself, i.e., the factor set W /∼. Moreover, both of these dependencies are strictly increasing functions of the variable q [10,25]. This fact, together with the partitioning of the input signals set into equivalence classes, allows for calculating the σ-entropy norm (19) of the system F 2 s = sup S(S) s Θ 2 in two steps: 1.…”

A Spectral Method of the Analysis of Linear Control Systems

“…The induced H 2 norm of the system with random input signals with limited mean anisotropy is called the anisotropic norm of the time invariant system. Within the framework of the anisotropy-based control theory the following common control problems were solved: optimal and suboptimal anisotropy-based control with uncertainties (Kurdyukov and Maximov, 2005;Kurdyukov et al, 2006), the generalization of the anisotropy-based control theory to descriptor systems (Belov et al, 2018;Belov and Andrianova, 2016), the anisotropy-based control theory in the case of a nonzero mathematical expectation of the input signal (Kurdyukov…”