Stability of singularly perturbed stochastic systems
type: Item
instance of: scholarly article
title: Stability of singularly perturbed stochastic systems
zbMATH Open document ID: 0922.93049
published in: Automation and Remote Control
publication date: 1999-10-17T00:00:00Z
review text: The author studies the rms stability of a linear singularly perturbed system of differential equations \[ dx=A_{11}(t)xdt+ A_{12}(t)ydt+ \bigl(B_{11} (t)x+B_{12}(t)y\bigr)dw \] \[ \varepsilon dy= A_{21} (t)xdt+ A_{22}(t)ydt +\sqrt \varepsilon\bigl(B_{21}(t)x+ B_{22}(t)y\bigr)dw \] whose coefficients are perturbed by a Gaussian white noise. The theory of integral manifolds of singularly perturbed systems is used to obtain the stability conditions. The effect of random forces on the stability of gyroscopic systems is discussed. The stability conditions are established. The possibility of replacing the complete equations of motion by the precession equations is considered, and a simple example shows that in the presence of the matrix of gyroscopic forces, the precession equations can provide an erroneous result.
Mathematics Subject Classification ID: 93E15
Mathematics Subject Classification ID: 93C73
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 70E05
zbMATH DE Number: 1263109
zbMATH Keywords: rms stability
zbMATH Keywords: linear singularly perturbed system
zbMATH Keywords: gyroscopic systems
zbMATH Keywords: precession equations
author: Elena Ya. Gorelova
reviewed by: Vasile Dragan
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1263109