Advances in Differential Equations and Control Processes

The Advances in Differential Equations and Control Processes is an esteemed international journal indexed in the Emerging Sources Citation Index (ESCI). It publishes original research articles related to recent developments in both theory and applications of ordinary and partial differential equations, integral equations, and control theory. The journal highlights the interdisciplinary nature of these topics, with applications in physical, biological, environmental, and health sciences, mechanics, and engineering. It also considers survey articles that identify future avenues of advancement in the field.

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SEMIADDITIVITY OF THE ENTROPY RAYLEIGH-RITZ OPERATOR IN THE PROBLEM OF REALIZATION OF AN INVARIANT POLYLINEAR REGULATOR OF A NON-STATIONARY HYPERBOLIC SYSTEM

Authors

  • V. A. Rusanov
  • A. V. Lakeyev
  • A. V. Daneev
  • Yu. É. Linke

Keywords:

nonlinear realization theory, non-stationary hyperbolic system, polylinear regulator, entropy Rayleigh-Ritz operator.

DOI:

https://doi.org/10.17654/0974324322020

Abstract

Such qualitative issues which bound up with existence of a solution for the inverse problem of systems analysis as realization solvability (sufficient conditions) of the operator functions of the polylinear regulator for a non-stationary hyperbolic system, which contains given (finite/countable/continual) nonlinear bundles of infinite-dimensional controlled dynamic processes in the capacity of admissible solutions in a separable Hilbert space, are investigated.

Received: February 23, 2022; Accepted: April 20, 2022;

References

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V. A. Rusanov, A. V. Daneev, Yu. É. Linke and P. A. Plesnyov, Existence of a bilinear delay differential realization of nonlinear neurodynamic process in the constructions of entropy Rayleigh-Ritz operator, Advances in Dynamical Systems and Applications 15(2) (2020), 199-215.

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V. A. Rusanov, R. A. Daneev, A. V. Lakeyev and Yu. É. Linke, Differential realization of second-order bilinear system: a functional geometric approach, Advances in Differential Equations and Control Processes 19(3) (2018), 303-321.

A. V. Daneev, A. V. Lakeyev and V. A. Rusanov, Existence of a bilinear differential realization in the constructions of tensor product of Hilbert spaces, WSEAS Trans. Math. 19 (2020), 99-107.

V. A. Rusanov, A. V. Daneev, A. V. Lakeyev and Yu. É. Linke, On the theory of differential realization: criteria of continuity of the nonlinear Rayleigh-Ritz operator, International Journal of Functional Analysis, Operator Theory and Applications 12(1) (2020), 1-22.

Published

2022-05-28

Issue

Section

Articles

How to Cite

SEMIADDITIVITY OF THE ENTROPY RAYLEIGH-RITZ OPERATOR IN THE PROBLEM OF REALIZATION OF AN INVARIANT POLYLINEAR REGULATOR OF A NON-STATIONARY HYPERBOLIC SYSTEM. (2022). Advances in Differential Equations and Control Processes, 27, 181-202. https://doi.org/10.17654/0974324322020

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