Scaling Laws for Disturbance Propagation in Cyclic Dynamical Networks

2015/02/03 by Milad Siami, Siami, Milad, Nader Motee +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Gene Regulatory Network Analysis #Neural Networks Stability and Synchronization #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1502.00926

openalex publication_date 2015/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Our goal is to analyze performance of stable linear dynamical networks subject to external stochastic disturbances. The square of the \mathcal H₂-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.

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