On the Stability of Stochastic Parametrically Forced Equations with Rank One Forcing
Dynamical Systems
2014-02-05 v1 Analysis of PDEs
Optimization and Control
Abstract
We derive simplified formulas for analyzing the stability of stochastic parametrically forced linear systems. This extends the results in [T. Blass and L.A. Romero, SIAM J. Control Optim. 51(2):1099--1127, 2013] where, assuming the stochastic excitation is small, the stability of such systems was computed using a weighted sum of the extended power spectral density over the eigenvalues of the unperturbed operator. In this paper, we show how to convert this to a sum over the residues of the extended power spectral density. For systems where the parametric forcing term is a rank one matrix, this leads to an enormous simplification.
Keywords
Cite
@article{arxiv.1402.0753,
title = {On the Stability of Stochastic Parametrically Forced Equations with Rank One Forcing},
author = {Timothy Blass and L. A. Romero and J. R. Torczynski},
journal= {arXiv preprint arXiv:1402.0753},
year = {2014}
}
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16 pages