Algorithms for sparse stable systems

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We deal with the problem of designing stable sparse decentralized systems. Whether the communication structure of a decentralized system can sustain stable dynamics can be reduced to the study of whether a given vector space of sparse matrices contains stable (Hurwitz) matrices. In this paper, after a brief overview the main known results in the area, we derive methods to create sparse stable vector space (that is, vector spaces that contain stable matrices) recursively and in polynomial time in the dimension of the space. The approach relies on perturbation theory to prove stability and on graph theory to derive polynomial time algorithms.

Original languageEnglish (US)
Title of host publication2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3457-3462
Number of pages6
ISBN (Print)9781467357173
DOIs
StatePublished - Jan 1 2013
Event52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy
Duration: Dec 10 2013Dec 13 2013

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other52nd IEEE Conference on Decision and Control, CDC 2013
CountryItaly
CityFlorence
Period12/10/1312/13/13

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ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Belabbas, M. A. (2013). Algorithms for sparse stable systems. In 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013 (pp. 3457-3462). [6760413] (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2013.6760413