Necessary condition for solvability of the control problem of an asynchronous spectrum of linear almost periodic systems with trivial averaging of the coefficient matrix
https://doi.org/10.29235/1561-2430-2019-55-2-176-181
Abstract
We consider a linear control system with an almost periodic matrix of coefficients. The control has a form of feedback and is linear in phase variables. It is assumed that the feedback coefficient is almost periodic and its frequency modulus, i.e. the smallest additive group of real numbers, including all Fourier exponents of this coefficient, is contained in the frequency module of the coefficient matrix.
The following problem is formulated: choose such a control from an admissible set so that the closed system has almost periodic solutions, the frequency spectrum (a set of Fourier exponents) of which contains a predetermined subset, and the intersection of the solution frequency modules and the coefficient matrix is trivial. The problem is called the control problem of the spectrum of irregular oscillations (asynchronous spectrum) with a target set of frequencies.
The aim of the work aws to obtain a necessary solvability condition for the control problem of the asynchronous spectrum of linear almost periodic systems with trivial averaging of coefficient matrix The estimate of the power of the asynchronous spectrum was found in the case of trivial averaging of the coefficient matrix.
Keywords
almost periodic linear systems,
trivial averaging,
Fourier exponents,
strongly irregular oscillations,
asynchronous spectrum
Supporting agencies: The work was carried out at the Institute of mathematics of the National academy of sciences of Belarus within the framework of the Belarusian Republican Foundation for Fundamental Research, project No. Ф18Р-014 “Robustness and stability loss of dynamic systems”.
About the Author
A. K. Demenchuk
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Aleksandr K. Demenchuk – Dr. Sc. (Physics and Mathematics), Assistant Professor, Leading Researcher of the Department of Differential Equations
11, Surganov Str., 220072, Minsk, Republic of Belarus
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