# Dzhalladova I. A.

### 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.

### Stochastic Lyapunov Functions for a System of Nonlinear Difference Equations

Ukr. Mat. Zh. - 2002. - 54, № 8. - pp. 1126

We study problems related to the stability of solutions of nonlinear difference equations with random perturbations of semi-Markov type. We construct Lyapunov functions for different classes of nonlinear difference equations with semi-Markov right-hand side and establish conditions for their existence.

### 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.

### On one method of factorization of polynomials

Ukr. Mat. Zh. - 1999. - 51, № 9. - pp. 1281–1286

We propose and justify a numerical method of factorization of polynomials with complex coefficients. We construct and algorithm of factorization of polynomials with real coefficients into real factors in the case of multiple roots.

### 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.

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

Ukr. Mat. Zh. - 1998. - 50, № 8. - pp. 1137–1143

We investigate a system of linear differential equations with random coefficients that depend on a periodic Markov process.

### Construction of a periodic system of moment equations

Ukr. Mat. Zh. - 1998. - 50, № 6. - pp. 774–780

We construct a system of moment equations for a system of linear differential equations with periodic coefficients.

### Investigation of stabilization of a mathematical model of a dynamical system with random influence in the resonance case

Ukr. Mat. Zh. - 1997. - 49, № 9. - pp. 1177–1181

We construct and investigate a mathematical model of a dynamical system with random influence stabilized by increasing the frequency of random influence.

### 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.