This article is cited in 4 papers

Stochastic Systems

Multiplicative stochastic systems with multiple external disturbances

M. E. Shaikin

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

Abstract: With the methods of $H_2/H_\infty$-control theory, in the presence of noise we solve the optimization problem for a multiplicative stochastic system with several external disturbances (the multiperturbation problem) and vector Wiener processes with arbitrary intensity matrices. We obtain matrix differential equations of Riccati type, reducing the original optimization problem to solving these equations.

Keywords: $H_2/H_\infty$-control theory, stochastic Ito equation, external disturbances, multiplicative system, optimization problem, Ito's formula, equation of Riccati type.

Presented by the member of Editorial Board: M. M. Khrustalev

Received: 24.04.2017

 English version: Automation and Remote Control, 2018, 79:2, 300–310

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