This article is cited in 1 paper

Differentical equations, dynamical systems and optimal control

Theorem on the existence of two-point oscillatory solutions to a relay perturbed system with a negative eigenvalue of the matrix

V. V. Yevstafyeva

Saint Petersburg State University, Universitetskaya nab., 7/9, 199034, St. Petersburg, Russia

Abstract: We consider a multidimensional system of ordinary first-order differential equations with a nonlinearity of a non-ideal relay and a continuous periodic function of perturbation in the right-hand side. The system matrix has simple, real, nonzero eigenvalues and at least one is negative. We study continuous oscillatory solutions with two switching points in phase space and with the same time of return to each of these points on the discontinuity surface. The theorem of both the existence of the solution and its parameters is established. An example illustrating the obtained theoretical results is given.

Keywords: $n$-dimensional ODE system, non-ideal relay, positive hysteresis, periodic function of perturbation, bounded solutions, switching points, periodicity on return time, simple real eigenvalues, nonsingular Lurie transformation, system of transcendental equations.

UDC: 517.925

MSC: 34C55, 34C25

Received January 14, 2023, published November 20, 2024

DOI: 10.33048/semi.2024.21.066