# Valeyev K. G.

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

Dzhalladova I. A., Valeyev K. G.

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.

### 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.

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.

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

Dzhalladova I. A., Valeyev K. G.

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.

### Optimization of Nonlinear Systems of Stochastic Difference Equations

Dzhalladova I. A., Valeyev K. G.

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.

### Criteria for the Asymptotic Stability of Solutions of Dynamical Systems

Dzhalladova I. A., Valeyev K. G.

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.

### Optimization of a system of linear differential equations with random coefficients

Dzhalladova I. A., Valeyev K. G.

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.

### Optimization of solutions of a linear control system

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.

### On one generalization of the averaging method

Dzhalladova I. A., Valeyev K. G.

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.

### Calculation of Bessel functions by using continued fractions

Kostinskii O. Ya., Valeyev K. G.

Ukr. Mat. Zh. - 1995. - 47, № 12. - pp. 1704–1705

We propose a new method for the calculation of Bessel functions of the first kind of integral order. By using the Laplace transformation, we solve a linear differential equation that defines the generating function for the Bessel functions expressed in terms of continued fractions.

### On the 75th birthday of Vyacheslav Alekseevich Dobrovol'skii

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

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

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

Karganyan I. R., Valeyev K. G.

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

### Numerical methods of constructing Lyapunov functions

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

### The metric theory of the Ostrogradskii algorithm

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

### Book reviews

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

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

### Generalization of the Gronwall - Bellman Lemma

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

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

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

### Investigation of stability in resonance cases

Valeyev K. G., Vazhgovskaya M. Ya.

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

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

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