2017
Том 69
№ 9

All Issues

Martynyuk A. A.

Articles: 22
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 (Russian)

Integral inequalities and stability of an equilibrium state on a time scale

Luk’yanova T. A., Martynyuk A. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 11. - pp. 1490–1499

We present some integral inequalities on a time scale and establish sufficient conditions for the uniform stability of an equilibrium state of a nonlinear system on a time scale.

Article (Russian)

On the mappings preserving the Lyapunov stability of Takagi–Sugeno fuzzy systems

Denisenko V. S., Martynyuk A. A., Slyn'ko V. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 5. - pp. 641-649

We propose a general principle of comparison for stability-preserving mappings and establish sufficient conditions of stability for the Takagi – Sugeno continuous fuzzy systems.

Article (Russian)

On the theory of stability of matrix differential equations

Lila D. M., Martynyuk A. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 4. - pp. 464-471

We establish the conditions of asymptotic stability of a linear system of matrix differential equations with quasiperiodic coefficients on the basis of constructive application of the principle of comparison with a Lyapunov matrix-valued function.

Article (Russian)

On stability of linear hybrid mechanical systems with distributed components

Martynyuk A. A., Slyn'ko V. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 2. - pp. 204–216

We present a new approach to the solution of problems of stability of hybrid systems based on the constructive determination of elements of a matrix-valued functional.

Anniversaries (Russian)

Aleksandr Mikhailovich Lyapunov (the 150th anniversary of his birth)

Martynyuk A. A., Mitropolskiy Yu. A.

Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 7. - pp. 996-1000

Article (English)

Stability analysis of large-scale functional differential systems

Martynyuk A. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 3. - pp. 382–394

The present paper is focused on a new method for analysis of stability of solutions of a large-scale functional differential system via matrix-valued Lyapunov-Krasovskii functionals. The stability conditions are based on information about the dynamical behavior of subsystems of the general system and properties of the functions of interconnection between them.

Article (Ukrainian)

Analytical construction of the hierarchical matrix Lyapunov function for impulse systems

Begmuratov K. A., Martynyuk A. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 4. - pp. 548–557

For impulse systems, we develop a method for the construction of the hierarchical matrix Lyapunov ffunction.

Article (Ukrainian)

Aleksandr Mikhailovich Lyapunov (the 125th anniversary of his birth)

Martynyuk A. A., Mitropolskiy Yu. A., Zubov V. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1982. - 34, № 4. - pp. 536—537

Article (Ukrainian)

Comparison principle for systems of differential equations with rapidly rotating phase

Martynyuk A. A., Matviichuk K. S.

Full text (.pdf)

Ukr. Mat. Zh. - 1979. - 31, № 5. - pp. 498–503

Article (Ukrainian)

Some problems in the comparison method in nonlinear mechanics

Martynyuk A. A., Mitropolskiy Yu. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1978. - 30, № 6. - pp. 823–829

Article (Ukrainian)

A theorem of lyapunov type concerning the stability of a multidimensional system

Martynyuk A. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1972. - 24, № 4. - pp. 532–537

Article (Ukrainian)

An iteration formula for Lyapunov-function construction

Martynyuk A. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1972. - 24, № 2. - pp. 253—258

Article (Ukrainian)

Sufficient conditions of stability of systems with steadily acting perturbations

Kozubovskaya I. G., Martynyuk A. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1971. - 23, № 3. - pp. 405–410

Article (Ukrainian)

Stability criterion for solutions of sets of nonlinear differential equations

Martynyuk A. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1971. - 23, № 2. - pp. 253–257

Article (Ukrainian)

On a rapidly converging iterational process for solving diffential equations and some of its applications

Martynyuk A. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1970. - 22, № 6. - pp. 734—748

Article (Ukrainian)

Polynomial approximations of the solutions of nonlinear equations

Martynyuk A. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1970. - 22, № 4. - pp. 557–563

Article (Ukrainian)

Construction of solutions of systems of differential equations in the region of asymptotic stability

Martynyuk A. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1970. - 22, № 3. - pp. 403–412

Brief Communications (Russian)

Construction of approximate solutions of denumerable systems and their stability

Martynyuk A. A., Sukennik A. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1969. - 21, № 5. - pp. 706–711

Brief Communications (Russian)

Sufficient conditions for stability in a finite system with delay

Kozubovskaya I. G., Martynyuk A. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1969. - 21, № 3. - pp. 399–406