Parametrization method for calculating exact stability bounds of stochastic linear systems with multiplicative noise
type: Item
instance of: scholarly article
title: Parametrization method for calculating exact stability bounds of stochastic linear systems with multiplicative noise
zbMATH Open document ID: 0870.93049
DOI: 10.1016/S0005-1098(96)80013-6
author: Juan-Miguel Gracia
published in: Automatica
publication date: 1997-03-06T00:00:00Z
review text: The authors investigate \(p\)-stability, that is, asymptotic stability (or for linear systems equivalently, exponential stability) of the \(p\)th moments of a linear stochastic system with multiplicative white noise, described by an Itô DE. Since, other than in the Stratonovich set-up, the trivial solutions of an Itô DE is 2-stable only if the drift matrix is stable, stability of the unperturbed system is assumed. The paper is concerned with finding the largest noise intensities which preserve first 2-stability, then \(p\)-stability, by means of solving an algebraic matrix equation associated with the deterministic linear DE for the covariance matrix \(Ex(t)x(t)^T\).
Mathematics Subject Classification ID: 93E15
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93D20
zbMATH DE Number: 988103
zbMATH Keywords: moment Lyapunov exponents
zbMATH Keywords: stochastic stability
zbMATH Keywords: \(p\)-stability
zbMATH Keywords: asymptotic stability
zbMATH Keywords: linear stochastic system
zbMATH Keywords: multiplicative white noise
reviewed by: Volker Wihstutz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 988103