DOI 10.17586/0021-3454-2018-61-6-469-476

DOI 10.17586/0021-3454-2018-61-6-469-476

**UDC 519.216:62.50:681.50.1**

## FORMATION OF CORRELATION MATRICES OF MULTICHANNEL DISCRETE SYSTEMS

ITMO University, Saint Petersburg, 197101, Russian Federation; postgraduete

P. I. Zaharova

ITMO University, Saint Petersburg, 197101, Russian Federation; postgraduate

A. S. Pavlov

ITMO University, Saint Petersburg, 197101, Russian Federation; postgraduate

A. V. Ushakov

ITMO University, Saint Petersburg, 197101, Russian Federation; Professor

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**Abstract.**For stochastic discrete external actions stationary in a broad sense, the problem of forming correlation matrices of state vectors and outputs of multichannel linear discrete systems is solved. Three methods for calculating the scalar correlation functions of the output of multichannel systems are presented. The first one allows to calculate the correlation function of an output, which depends on the scalar stochastic effect on a particular input; the second is used to calculate the correlation functions of each output of the system under the vector stochastic action; the third one forms the minorant and the majorant of the correlation func-tions of the system in the space of its outputs by means of singular expansion of the correlation matrix. It is shown that the problem of forming correlation matrices and functions can be solved based on using the fundamental matrices of the system under the condition that the matrix of dispersions of the state vector is known. The state space method allows calculation of the dispersions matrix of the system state vector using the discrete Lyapunov matrix equation in the case of an exogenous stochastic effect of the discrete "white noise" type. The developed procedures for formation of correlation matrices of vector variables of discrete multichannel systems are illustrated by examples.

**Keywords:**discrete stochastic effect, discrete system, discrete Lyapunov equation, fundamental matrix, correlation matrix (function)

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