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UDC 517.9

CONCERNING AN INTEGRATED VARIETY MODIFICATION METHOD IN CONTROL SYSTEMS

M. I. Kuptsov, PhD, Chief of Mathematics and Information Technology Department, the Academy of the Federal Penal Service of Russia; This email address is being protected from spambots. You need JavaScript enabled to view it.
V. V. Tenyaev, PhD, Vice Chief of Mathematics and Information Technology Department, the Academy of the Federal Penal Service of Russia; This email address is being protected from spambots. You need JavaScript enabled to view it.
I. M. Kuptsov, MIPT student; This email address is being protected from spambots. You need JavaScript enabled to view it.

The problem is to find nonzero integrated variety of ordinary differential equations nonlinear finitedimensional system where the right hand side is a periodic vector function using argument and containing parameter. Presumably, the system under investigation has trivial integrated variety with all parameter points while corresponding linear subsystem does not have exponential dichotomous attribute. The aim of the article is to find sufficient criterion in the neighborhood condition of nonzero integrated variety of less dimension than in original phase space. That is why on the base of integrated variety classic method ideas the operators which enable us to solve the problems of their fixed points search are made. According to the analyzed system specification, the integrated variety method of operator equations formation has been considerably
modified.

Key words: integrated variety method, ordinary differential equations system, operator equation, dimensional reduction of phase space, control systems.

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