Open AccessTO EXISTENCE OF COMPLETELY CONTINUOUS DIFFERENTIAL REALIZATION SECOND ORDER BILINEAR SYSTEM
Author(s) -
A. V. Daneev,
AUTHOR_ID,
А. В. Лакеев,
В. А. Русанов,
AUTHOR_ID,
AUTHOR_ID
Publication year - 2021
Publication title -
izvestiâ samarskogo naučnogo centra rossijskoj akademii nauk
Language(s) - English
Resource type - Journals
ISSN - 1990-5378
DOI - 10.37313/1990-5378-2021-23-4-116-132
Subject(s) - mathematics , realization (probability) , nonlinear system , separable space , bilinear interpolation , mathematical analysis , hilbert space , differential operator , order (exchange) , differential equation , pure mathematics , physics , statistics , finance , quantum mechanics , economics
For a continuous nonlinear infinite-dimensional behavioristic system (dynamical system of J. Willems), a functional-geometric study of the necessary and sufficient conditions for the existence of six non-stationary coefficients-operators of the model of bilinear differential realization of this system in the class of second-order differential equations in a separable Hilbert space is carried out. The case is investigated when the simulated operators are burdened with a condition that ensures the complete continuity of the integral form of the equations of realization in the entropy setting.