2019
Том 71
№ 8

All Issues

Lapshin A. L.

Articles: 5
Article (Russian)

Equations for second moments of solutions of a system of linear differential equations with random semi-Markov coefficients and random input

Lapshin A. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 6. - pp. 776–783

We derive equations that determine second moments of a random solution of a system of Itô linear differential equations with coefficients depending on a finite-valued random semi-Markov process. We obtain necessary and sufficient conditions for the asymptotic stability of solutions in the mean square with the use of moment equations and Lyapunov stochastic functions.

Article (Russian)

The correlation matrix of random solutions of a dynamical system with Markov coefficients

Lapshin A. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 3. - pp. 338–348

For dynamical systems which are described by systems of differential or difference equations dependent on a finite-valued Markov process, we suggest a new form of equations for moments of their random solution. We derive equations for a correlation matrix of random solutions.

Brief Communications (Russian)

Filtration and prediction of random solutions of a system of linear differential equations with coefficients depending on a finite-valued Markov process

Lapshin A. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 7. - pp. 997–1000

We obtain an equation of optimal filtration for processes of Markov random evolution, which is a solution of systems of linear differential equations with Markov switchings.

Brief Communications (Russian)

Filtration of random solutions of a system of linear difference equations with coefficients depending on a Markov chain

Lapshin A. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 4. - pp. 590–592

We solve the problem of the estimation of a random state for a system with discrete time that is described by a system of linear difference equations with coefficients depending on a finite-valued Markov chain.

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.