MATHEMATICS

Asymptotic approximations of a solution of one class of linear time-varying singularly perturbed systems with constant delay

O. B. Tsekhan

Yanka Kupala State University of Grodno, ul. Ozheshko, 22, Grodno, 230023, Belarus

Abstract: For a linear time-varying singularly perturbed control system with constant state delay in the equation for slow variables (LTVSPSD), a method for constructing asymptotic approximations of solutions has been developed based on the representation of the right-hand side operator of the system in a ring of polynomials in the delay operator, embedding the LTVSPSD into a family of systems in the extended state space, and applying non-degenerate transformations. Asymptotic approximations of zero and first orders of the solution of the Cauchy problem for the LTVSPSD are constructed.

Keywords: singularly perturbed system, time-varying system, delay, asymptotic approximation, solution

UDC: 517.928, 517.929

MSC: 34K26, 34K17, 41A60

Received: 28.08.2024
Accepted: 09.12.2025

DOI: 10.35634/vm250405

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