2014/02/04 by Blass, Timothy, Romero, L. A., Torczynski, J. R.
#34D10 #60H10 #60H15 #76E17 (Secondary) #93E15 (Primary) #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.1402.0753
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.