2019
Том 71
№ 5

All Issues

Valeyev K. G.

Articles: 17
Brief Communications (Russian)

Second-order moment equations for a system of differential equations with random right-hand side

Dzhalladova I. A., Valeyev K. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 5. - pp. 687-691

We present a method for the derivation of second-order moment equations for solutions of a system of nonlinear equations that depends on a finite-valued semi-Markov or Markov process. For systems of linear differential equations with random coefficients, the case where the inhomogeneous part contains white noise is considered.

Brief Communications (Ukrainian)

Derivation of Moment Equations for Solutions of a System of Nonlinear Difference Equations Dependent on a Semi-Markov Process

Dzhalladova I. A., Valeyev K. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 6. - pp. 858-864

We propose a method for the derivation of moment equations for solutions of a system of nonlinear difference equations that depends on a finite-valued semi-Markov process. For systems of linear equations, we compare the results obtained with known ones.

Brief Communications (Russian)

Derivation of Moment Equations for Solutions of a System of Differential Equations Dependent on a Semi-Markov Process

Dzhalladova I. A., Valeyev K. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 11. - pp. 1569-1573

We present a new method for the derivation of moment equations for solutions of a system of nonlinear differential equations dependent on a finite-valued semi-Markov process. For systems of linear equations, we compare the results obtained with known ones.

Article (Russian)

Optimization of Nonlinear Systems of Stochastic Difference Equations

Dzhalladova I. A., Valeyev K. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 1. - pp. 3-14

We present new results concerning the synthesis of optimal control for systems of difference equations that depend on a semi-Markov or Markov stochastic process. We obtain necessary conditions for the optimality of solutions that generalize known conditions for the optimality of deterministic systems of control. These necessary optimality conditions are obtained in the form convenient for the synthesis of optimal control. On the basis of Lyapunov stochastic functions, we obtain matrix difference equations of the Riccati type, the integration of which enables one to synthesize an optimal control. The results obtained generalize results obtained earlier for deterministic systems of difference equations.

Brief Communications (Russian)

Criteria for the Asymptotic Stability of Solutions of Dynamical Systems

Dzhalladova I. A., Valeyev K. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 12. - pp. 1702-1707

We present a new proof for criteria for the asymptotic stability of systems of difference and differential equations based on the properties of monotone operators in a semiordered space. We also establish necessary and sufficient conditions for the asymptotic stability of stochastic systems of differential and difference equations in the mean square.

Brief Communications (Russian)

Optimization of a system of linear differential equations with random coefficients

Dzhalladova I. A., Valeyev K. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 4. - pp. 556–561

We consider a system of differential equations with controls that are linearly contained in the right-hand sides. We establish a necessary condition for the optimal control that minimizes a quadratic functional.

Brief Communications (Russian)

Optimization of solutions of a linear control system

Lapshin A. L., Valeyev K. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 10. - pp. 1429–1431

We suggest a new method for optimizing solutions of a linear control system, which is based on the solution of the Lyapunov matrix equation.

Article (Russian)

On one generalization of the averaging method

Dzhalladova I. A., Valeyev K. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 7. - pp. 906–911

We consider one case where it is possible to establish sufficient conditions for the convergence and analyticity of matrix series used for the construction of a system of moment equations.

Anniversaries (Ukrainian)

On the 75th birthday of Vyacheslav Alekseevich Dobrovol'skii

Bogolyubov A. N., Tamrazov P. M., Valeyev K. G.

Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 10. - pp. 1409

Article (Ukrainian)

Reduction of a canonical system of linear differential equations with periodic coefficients

Karganyan I. R., Valeyev K. G.

Full text (.pdf)

Ukr. Mat. Zh. - 1977. - 29, № 5. - pp. 637–642

Article (Ukrainian)

Numerical methods of constructing Lyapunov functions

Valeyev K. G.

Full text (.pdf)

Ukr. Mat. Zh. - 1976. - 28, № 1. - pp. 3–11

Article (Ukrainian)

The metric theory of the Ostrogradskii algorithm

Valeyev K. G., Zlebov Ye. D.

Full text (.pdf)

Ukr. Mat. Zh. - 1975. - 27, № 1. - pp. 64–69

Article (Ukrainian)

Book reviews

Valeyev K. G., Volosov V. M., Zhautykov O. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1974. - 26, № 6. - pp. 855–856

Article (Ukrainian)

Generalization of the Gronwall - Bellman Lemma

Valeyev K. G.

Full text (.pdf)

Ukr. Mat. Zh. - 1973. - 25, № 4. - pp. 518—521

Article (Ukrainian)

Using an asymptotic method in the critical case of a double zero root

Valeyev K. G.

Full text (.pdf)

Ukr. Mat. Zh. - 1971. - 23, № 3. - pp. 364–367

Article (Ukrainian)

Investigation of stability in resonance cases

Valeyev K. G., Vazhgovskaya M. Ya.

Full text (.pdf)

Ukr. Mat. Zh. - 1971. - 23, № 1. - pp. 63–70

Article (Ukrainian)

Family of solutions with a finite number of parameters of a system of differential equations with deviating argument

Kulesko N. A., Valeyev K. G.

Full text (.pdf)

Ukr. Mat. Zh. - 1968. - 20, № 6. - pp. 739–749