Frequency analysis and norms of distributed spatially periodic systems

Makan Fardad, Mihailo R. Jovanovic, Bassam Bamieh

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

We investigate several fundamental aspects of the theory of linear distributed systems with spatially periodic coefficients. We develop a spatial-frequency domain representation analogous to the lifted or frequency response operator representation for linear time periodic systems. Using this representation, we introduce the notion of the H2 norm for this class of systems and provide algorithms for its computation. A stochastic interpretation of the H2 norm is given in terms of spatially cyclostationary random fields and spectral-correlation density operators. When the periodic coefficients are viewed as feedback modifications of spatially invariant systems, we show how they can stabilize or destabilize the original systems in a manner analogous to vibrational control or parametric resonance in time periodic systems. Two examples from physics are provided to illustrate the main results.

Original languageEnglish (US)
Pages (from-to)2266-2279
Number of pages14
JournalIEEE Transactions on Automatic Control
Volume53
Issue number10
DOIs
StatePublished - 2008

Fingerprint

Time varying systems
Frequency response
Mathematical operators
Physics
Feedback

Keywords

  • Cyclostationary random fields
  • Frequency domain lifting
  • Frequency response opertators
  • H2 norm
  • Partial differential equation (PDE) with periodic coefficients
  • Spatially periodic systems

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Computer Science Applications

Cite this

Frequency analysis and norms of distributed spatially periodic systems. / Fardad, Makan; Jovanovic, Mihailo R.; Bamieh, Bassam.

In: IEEE Transactions on Automatic Control, Vol. 53, No. 10, 2008, p. 2266-2279.

Research output: Contribution to journalArticle

Fardad, Makan ; Jovanovic, Mihailo R. ; Bamieh, Bassam. / Frequency analysis and norms of distributed spatially periodic systems. In: IEEE Transactions on Automatic Control. 2008 ; Vol. 53, No. 10. pp. 2266-2279.
@article{99dcfe01da4f47138917de260dac91cc,
title = "Frequency analysis and norms of distributed spatially periodic systems",
abstract = "We investigate several fundamental aspects of the theory of linear distributed systems with spatially periodic coefficients. We develop a spatial-frequency domain representation analogous to the lifted or frequency response operator representation for linear time periodic systems. Using this representation, we introduce the notion of the H2 norm for this class of systems and provide algorithms for its computation. A stochastic interpretation of the H2 norm is given in terms of spatially cyclostationary random fields and spectral-correlation density operators. When the periodic coefficients are viewed as feedback modifications of spatially invariant systems, we show how they can stabilize or destabilize the original systems in a manner analogous to vibrational control or parametric resonance in time periodic systems. Two examples from physics are provided to illustrate the main results.",
keywords = "Cyclostationary random fields, Frequency domain lifting, Frequency response opertators, H2 norm, Partial differential equation (PDE) with periodic coefficients, Spatially periodic systems",
author = "Makan Fardad and Jovanovic, {Mihailo R.} and Bassam Bamieh",
year = "2008",
doi = "10.1109/TAC.2008.2006104",
language = "English (US)",
volume = "53",
pages = "2266--2279",
journal = "IEEE Transactions on Automatic Control",
issn = "0018-9286",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "10",

}

TY - JOUR

T1 - Frequency analysis and norms of distributed spatially periodic systems

AU - Fardad, Makan

AU - Jovanovic, Mihailo R.

AU - Bamieh, Bassam

PY - 2008

Y1 - 2008

N2 - We investigate several fundamental aspects of the theory of linear distributed systems with spatially periodic coefficients. We develop a spatial-frequency domain representation analogous to the lifted or frequency response operator representation for linear time periodic systems. Using this representation, we introduce the notion of the H2 norm for this class of systems and provide algorithms for its computation. A stochastic interpretation of the H2 norm is given in terms of spatially cyclostationary random fields and spectral-correlation density operators. When the periodic coefficients are viewed as feedback modifications of spatially invariant systems, we show how they can stabilize or destabilize the original systems in a manner analogous to vibrational control or parametric resonance in time periodic systems. Two examples from physics are provided to illustrate the main results.

AB - We investigate several fundamental aspects of the theory of linear distributed systems with spatially periodic coefficients. We develop a spatial-frequency domain representation analogous to the lifted or frequency response operator representation for linear time periodic systems. Using this representation, we introduce the notion of the H2 norm for this class of systems and provide algorithms for its computation. A stochastic interpretation of the H2 norm is given in terms of spatially cyclostationary random fields and spectral-correlation density operators. When the periodic coefficients are viewed as feedback modifications of spatially invariant systems, we show how they can stabilize or destabilize the original systems in a manner analogous to vibrational control or parametric resonance in time periodic systems. Two examples from physics are provided to illustrate the main results.

KW - Cyclostationary random fields

KW - Frequency domain lifting

KW - Frequency response opertators

KW - H2 norm

KW - Partial differential equation (PDE) with periodic coefficients

KW - Spatially periodic systems

UR - http://www.scopus.com/inward/record.url?scp=52449115651&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=52449115651&partnerID=8YFLogxK

U2 - 10.1109/TAC.2008.2006104

DO - 10.1109/TAC.2008.2006104

M3 - Article

VL - 53

SP - 2266

EP - 2279

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 10

ER -