A perturbation analysis of parametric resonance and periodic control in spatially distributed systems

Makan Fardad, Bassam Bamieh

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

4 Scopus citations

Abstract

We consider a class of spatially distributed systems with spatially periodic coefficients that enter the system as perturbation. We then analyze the stability properties of the system for various frequencies of the perturbation. We show that, up to first order in the perturbation amplitude, parametric resonance can only occur at the isolated frequency equal to twice the frequency of the marginally-stable mode of the unperturbed system. Finally, we derive explicit expressions for the perturbation expansion of the marginally-stable mode, for all frequencies of the perturbation, and show how strict stability can be achieved for an appropriate choice of the perturbation.

Original languageEnglish (US)
Title of host publication2004 43rd IEEE Conference on Decision and Control (CDC)
Pages3786-3791
Number of pages6
DOIs
StatePublished - Dec 1 2004
Externally publishedYes
Event2004 43rd IEEE Conference on Decision and Control (CDC) - Nassau, Bahamas
Duration: Dec 14 2004Dec 17 2004

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume4
ISSN (Print)0191-2216

Other

Other2004 43rd IEEE Conference on Decision and Control (CDC)
CountryBahamas
CityNassau
Period12/14/0412/17/04

ASJC Scopus subject areas

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

Cite this

Fardad, M., & Bamieh, B. (2004). A perturbation analysis of parametric resonance and periodic control in spatially distributed systems. In 2004 43rd IEEE Conference on Decision and Control (CDC) (pp. 3786-3791). [ThC04.5] (Proceedings of the IEEE Conference on Decision and Control; Vol. 4). https://doi.org/10.1109/CDC.2004.1429328