Article

Received 14.09.2021

Revised 08.01.2022

Accepted 15.02.2022

Retrieved from Vol. 26, No. 1, 2022

Pages 48 -54

Vyshenska, О. (2022). On the existence of an invariant torus of one class of discontinuous dynamical systems. The National Transport University Bulletin, 26(1), 48-54. https://doi.org/10.33744/2308-6645-2022-1-51-048-054

On the existence of an invariant torus of one class of discontinuous dynamical systems

О. Vyshenska

A system of differential equations with discontinuous trajectories is considered. The need to study such systems is associated primarily with the demands of the latest technology, where pulse automatic control systems, pulse computing systems have taken a very prominent place and are being intensively developed, expanding the range of their applications in technical problems that are heterogeneous in physical nature and functional purpose. Sufficient conditions for the existence and asymptotic stability of the invariant set of a dynamical system subjected to impulsive action are formulated. Theorem. If for the matrix A(φ) the corresponding condition is fulfilled, then for a sufficiently small Lipschitz constant N the system of equations has an asymptotically stable invariant set, where u(φ) is a piecewise continuous function with discontinuities of the first kind as φ ∈ Г.

 

differential equations; impulsive action; asymptotic stability
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https://doi.org/10.33744/2308-6645-2022-1-51-048-054