Scaling Laws for Disturbance Propagation in Cyclic Dynamical Networks
arXiv:1502.00926
Abstract
Our goal is to analyze performance of stable linear dynamical networks subject to external stochastic disturbances. The square of the -norm of the network is used as a performance measure to quantify the expected steady-state dispersion of the outputs of the network. We show that this performance measure can be tightly bounded from below and above by some spectral functions of the state-space matrices of the network. This result is applied to a class of cyclic linear networks and shown that their performance measure scale quadratically with the network size.
14 pages; submitted for possible journal publication. arXiv admin note: text overlap with arXiv:1403.1494