Solvability of the control problem of the asynchronous spectrum of linear almost periodic systems with a lower triangular representation of the averaging of coefficient matrix
https://doi.org/10.29235/1561-8323-2021-65-3-263-268
Abstract
A linear control system with an almost periodic matrix of coefficients and control in the form of the feedback linear in phase variables is considered. It is assumed that the feedback coefficient is almost periodic and its frequency module, i. e. the smallest additive group of real numbers, including all the Fourier exponents of this coefficient, is contained in the frequency module of the coefficient matrix. The system under consideration is studied in the case of a triangular average value of the matrix of coefficients. For the described class of systems, the control problem of the asynchronous spectrum with a target set of frequencies is solved. This task is to construct such a control from an admissible set that the system closed by this control has almost periodic solutions, a set of the Fourier exponents of which contains a predetermined subset, and the intersection of the solution frequency modules and the coefficient matrix is trivial. The necessary and sufficient conditions for the solvability of this problem are obtained.
About the Author
A. K. Demenchuk
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Aleksandr K. Demenchuk – D. Sc. (Physics and Mathematics), Assistant Professor, Chief Researcher
11, Surganov Str., Minsk, 220072, Republic of Belarus
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