Parametrization method for calculating exact stability bounds of stochastic linear systems with multiplicative noise (Q675289)

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 \(Ex(t)x(t)^T\).