2019
Том 71
№ 11

All Issues

Khusainov D. Ya.

Articles: 19
Anniversaries (Ukrainian)

Oleksandr Mykolaiovych Sharkovs’kyi (on his 80th birthday)

Fedorenko V. V., Ivanov А. F., Khusainov D. Ya., Kolyada S. F., Maistrenko Yu. L., Parasyuk I. O., Pelyukh G. P., Romanenko O. Yu., Samoilenko V. G., Shevchuk I. A., Sivak A. G., Tkachenko V. I., Trofimchuk S. I.

Full text (.pdf)

Ukr. Mat. Zh. - 2017. - 69, № 2. - pp. 257-260

Article (Russian)

Stability of one difference equation with positive coefficients

Khusainov D. Ya., Nikiforova N. S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 9. - pp. 1276–1280

We consider a linear homogeneous difference equation of ordern with positive coefficients, which is presented in the normal form. We obtain necessary and sufficient conditions for the stability and asymptotic stability.

Brief Communications (Russian)

Stability of difference rational systems

Khusainov D. Ya., Shevelenko E. E.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 3. - pp. 428–431

For systems of difference equations with rational functions on the right-hand sides represented in a unified vector matrix form, we obtain stability conditions and calculate a value of the radius of a disk for the domain of asymptotic stability on the basis of the second Lyapunov method.

Article (Russian)

Control over a linear system up to a given Lyapunov function

Khusainov D. Ya., Kozhametov A. T.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 10. - pp. 1409–1415

We obtain control conditions for a linear system whose Lyapunov functions satisfy certain conditions.

Article (Russian)

Stability of differential systems with rational right-hand sides

Khusainov D. Ya., Shevelo V. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1995. - 47, № 9. - pp. 1295–1299

We prove theorems which establish estimates for the domain of stability of a differential system with rational right-hand side. We also construct estimates of the convergence of solutions of the system.

Brief Communications (Russian)

Robust stability of systems with delay

Khusainov D. Ya., Mustafaeva R.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1995. - 47, № 6. - pp. 859–863

We consider linear stationary systems of differential equations with delay. The matrices that determine the dynamics of a system vary within a certain interval. We obtain sufficient conditions for the robust stability of systems uniform with respect to delay and depending on the deviation of the argument.

Article (Russian)

Stability estimates for linear stochastic systems with deviating argument of neutral type

Bychkov A. S., Khusainov D. Ya.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 6. - pp. 834–842

We study linear stochastic differential equations with deviating argument of neutral type and establish sufficient conditions of stability. The functions determining the initial perturbations of solutions are found.

Brief Communications (Russian)

Estimates of stability of desynchronized systems

Khusainov D. Ya., Stadnik O. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 1. - pp. 148–152

Linear difference systems with lag are considered. The sufficient conditions of stability are established and exponential decay coefficients for solutions are derived. The second Lyapunov method with Razumikhin's condition is used.

Article (Ukrainian)

Investigation of stability conditions of stochastical perturbed systems with lag

Khusainov D. Ya., Nechaeva I. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1992. - 44, № 8. - pp. 1060–1064

Linear stochastic differential systems with a single lag are considered. Sufficient conditions for uniform (in lag) stability in the mean-square under constantly acting perturbations are obtained.

Article (Ukrainian)

Stability estimates of solutions of systems of functional-differential equations of neutral type

Khusainov D. Ya.

Full text (.pdf)

Ukr. Mat. Zh. - 1991. - 43, № 9. - pp. 1123–1135

Article (Ukrainian)

Exponential estimates of solutions of linear stochastic differential functional equations

Khusainov D. Ya., Nechaeva I. G.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 10. - pp. 1338–1343

Article (Ukrainian)

Absolute stability of control systems with retarded argument

Khusainov D. Ya., Shatyrko A. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 2. - pp. 245–249

Article (Ukrainian)

Closeness of the solutions of linear systems with delay and their corresponding systems without delay

Khusainov D. Ya., Yun'kova E. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 11. - pp. 1549–1552

Article (Ukrainian)

Stability estimates of linear stochastic systems

Khusainov D. Ya., Kozhametov A. T.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 9. - pp. 1267–1273

Article (Ukrainian)

Stability of neutral-type nonlinear control systems

Khusainov D. Ya., Zhuikova A. G.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 6. - pp. 848–853

Article (Ukrainian)

A method of determination of the solution of Lyapunov's equation with a prescribed spectrum

Khusainov D. Ya., Yun'kova E. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1984. - 36, № 4. - pp. 528 – 531

Article (Ukrainian)

Some remarks on the extremal Lyapunov function for linear systems

Khusainov D. Ya., Komarov Yu. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1983. - 35, № 6. - pp. 750–753

Article (Ukrainian)

Estimation of magnitude of retardation in linear differential systems with deviated argument

Khusainov D. Ya., Yun'kova E. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1983. - 35, № 2. - pp. 261—254

Article (Ukrainian)

Some generalizations of Lyapunov's second method

Khusainov D. Ya., Tsitritsky O. Ye.

Full text (.pdf)

Ukr. Mat. Zh. - 1976. - 28, № 2. - pp. 287–271