Martynyuk A. A.
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.
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.
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.
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.
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.
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.
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.
Ukr. Mat. Zh. - 2007. - 59, № 7. - pp. 996-1000
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.
Ukr. Mat. Zh. - 1999. - 51, № 11. - pp. 1476–1484
The asymptotic stability with respect to two measures of impulsive systems under structural perturbations is investigated. Conditions of asymptotic (ρ0, ρ)-stability of the system in terms of the fixed signs of some special matrices are established.
Ukr. Mat. Zh. - 1999. - 51, № 6. - pp. 784–795
The stability and asymptotic stability of solutions of large-scale linear impulsive systems under structural perturbations are investigated. Sufficient conditions for stability and instability are formulated in terms of the fixed signs of special matrices.
Ukr. Mat. Zh. - 1999. - 51, № 2. - pp. 204–213
We study the problem of $μ$-stability of a dynamical system with delay. Conditions of the practical $μ$-stability are established for the general case and for a quasilinear system. The conditions suggested are illustrated by an example.
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.
Ukr. Mat. Zh. - 1996. - 48, № 10. - pp. 1352-1362
By using the matrix Lyapunov function, we establish conditions of (uniform) stability and (uniform) asymptotic stability of a large-scale discrete system under structural perturbations.
Ukr. Mat. Zh. - 1996. - 48, № 5. - pp. 642-649
We establish conditions of exponentialx 1-stability and polystability for systems with separable motions. Stability conditions of these types are obtained by using the Lyapunov functions (scalar and matrix).
Ukr. Mat. Zh. - 1982. - 34, № 4. - pp. 536—537
Ukr. Mat. Zh. - 1979. - 31, № 5. - pp. 498–503
Ukr. Mat. Zh. - 1978. - 30, № 6. - pp. 823–829
Ukr. Mat. Zh. - 1972. - 24, № 4. - pp. 532–537
Ukr. Mat. Zh. - 1972. - 24, № 2. - pp. 253—258
Ukr. Mat. Zh. - 1971. - 23, № 3. - pp. 405–410
Ukr. Mat. Zh. - 1971. - 23, № 2. - pp. 253–257
On a rapidly converging iterational process for solving diffential equations and some of its applications
Ukr. Mat. Zh. - 1970. - 22, № 6. - pp. 734—748
Ukr. Mat. Zh. - 1970. - 22, № 4. - pp. 557–563
Construction of solutions of systems of differential equations in the region of asymptotic stability
Ukr. Mat. Zh. - 1970. - 22, № 3. - pp. 403–412
Ukr. Mat. Zh. - 1969. - 21, № 5. - pp. 706–711
Ukr. Mat. Zh. - 1969. - 21, № 3. - pp. 399–406