TY - GEN
T1 - A perturbation analysis of parametric resonance and periodic control in spatially distributed systems
AU - Fardad, Makan
AU - Bamieh, Bassam
PY - 2004
Y1 - 2004
N2 - 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.
AB - 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.
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U2 - 10.1109/CDC.2004.1429328
DO - 10.1109/CDC.2004.1429328
M3 - Conference contribution
AN - SCOPUS:14244260553
SN - 0780386825
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 3786
EP - 3791
BT - 2004 43rd IEEE Conference on Decision and Control (CDC)
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2004 43rd IEEE Conference on Decision and Control (CDC)
Y2 - 14 December 2004 through 17 December 2004
ER -