2019
Том 71
№ 2

All Issues

Martynyuk-Chernienko Yu. A.

Articles: 5
Article (Russian)

Analysis of the Set of Trajectories of Fuzzy Equations of Perturbed Motion

Martynyuk A. A., Martynyuk-Chernienko Yu. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 11. - pp. 1512–1527

The paper presents a new approach to the investigation of the first-order fuzzy initial-value problems. We use different versions of the comparison principle to establish conditions for the existence of solutions of a set of differential equations.

Article (Russian)

Existence, uniqueness, and estimation of solutions for a set of equations of perturbed motion

Martynyuk A. A., Martynyuk-Chernienko Yu. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 2. - pp. 273-295

We propose a regularization procedure for a set of equations of perturbed motion with uncertain values of parameters. Using the comparison principle, we establish conditions for the existence of solutions of the original system and the regularized system.

Article (Russian)

Stability of motion of nonlinear systems with fuzzy characteristics of parameters

Martynyuk A. A., Martynyuk-Chernienko Yu. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 1. - pp. 50-70

We investigate the stability of a stationary solution of a fuzzy dynamical system by a generalized Lyapunov direct method.

Article (Ukrainian)

On the theory of stability of motion of a nonlinear system on a time scale

Martynyuk-Chernienko Yu. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 6. - pp. 776–782

We investigate the problem of stability of a nonlinear system on a time scale and propose a unified approach to the analysis of stability of motion based on a generalized direct Lyapunov method.

Article (Russian)

On the stability of solutions of a quasilinear uncertain system

Martynyuk-Chernienko Yu. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 4. - pp. 458–465

We generalize the Lyapunov direct method, which can be used for establishing new conditions of the uniform asymptotic stability of solutions of an uncertain system with respect to an invariant moving set.