Year: 2013
Type: preprint
Abstract: In the design of decentralized networked systems, it is useful to know whether a given network topology can sustain stable dynamics. We consider a basic version of this problem here: given a vector space of sparse real matrices, does it contain a stable (Hurwitz) matrix? Said differently, is a feedback channel (corresponding to a non-zero entry) necessary for stabilization or can it be done without. We provide in this paper a set of necessary and a set of sufficient conditions for the existence of stable matrices in a vector space of sparse matrices. We further prove some properties of the set of sparse matrix spaces that contain Hurwitz matrices. The conditions we exhibit are most easily stated in the language of graph theory, which we thus adopt in this paper.
Source: arXiv (Cornell University)
Author: Belabbas, M. -A .
Institution: University of Illinois Urbana-Champaign
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1495955040