Necessary condition of solvability of the control problem of the asynchronous spectrum of linear periodic systems with non-degenerate matrix in control in non-resonant case
https://doi.org/10.67268/1812-5093-2026-34-1-76-84
EDN: DQVILP
Abstract
A linear periodic system with a constant non-degenerate matrix under control is considered. The program control is periodic, and its period is incommensurable with the period of the coefficient matrix. The admissible set of such periodic controls is called irregular. The problem is to choose such a control from this admissible set so that the now quasi-periodic system has a partially irregular periodic solution with a given frequency spectrum whose period coincides with the period of the control. Such problem is called the control problem of the asynchronous spectrum with an irregular admissible set. To solve it, the original system is reduced to some linear nonhomogeneous system of lower dimension. The non-resonant case is studied, when the corresponding homogeneous system has no irregular periodic solutions. A necessary condition for the solvability of the control problem of the asynchronous spectrum with an irregular admissible set is obtained.
About the Authors
A. K. Demenchuk
Institute of Mathematic of the National Academy of Sciences of Belarus
Belarus
Belarus
Minsk
E. K. Makarov
Institute of Mathematic of the National Academy of Sciences of Belarus
Belarus
Belarus
Minsk
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Review
For citations:
Demenchuk A.K., Makarov E.K. Necessary condition of solvability of the control problem of the asynchronous spectrum of linear periodic systems with non-degenerate matrix in control in non-resonant case. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2026;34(1):76-84. (In Russ.) https://doi.org/10.67268/1812-5093-2026-34-1-76-84. EDN: DQVILP
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