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Advances in Statistical Control, Algebraic Systems Theory, and Dynamic Systems Characteristics pp 223–244Cite as

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Characterization and Calculation of Approximate Decentralized Fixed Modes (ADFMs)

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Part of the book series: Systems & Control: Foundations & Applications ((SCFA))

Summary

It is well known that a linear time-invariant (LTI) system can be stabilized using decentralized LTI control if and only if the system does not possess any unstable decentralized fixed modes (DFMs). However, in industrial system application studies, it often is the case that a system has no DFMs, but may have approximate DFMs (ADFMs), which are modes that are not DFMs, but are “close” to being DFMs; in particular, such ADFMs can be divided into two types: “structured” ADFMs and “unstructured” ADFMs.In general ADFMs have the property that, although they are not fixed, they may require a “huge control energy” to shift the modes to desirable regions of the complex plane, which may be impossible to obtain. It is thus important to be able to characterize and determine what modes of a system, if any, are ADFMs, and this is the focus of the chapter. A number of industrial application problems will be used to demonstrate the effectiveness of the proposed algorithms for the calculation of ADFMs and to illustrate the properties of these ADFMs.

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References

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Author information

Authors and Affiliations

  1. Dept. of Elect. and Comp. Eng, University of Toronto, Toronto, Ontario M5S 1A4, Canada

    Edward J. Davison

  2. Dept. of Elect. and Comp Eng., Concordia University, Montreal, Quebec H3G 1M8, Canada

    Amir G. Aghdam

Authors
  1. Edward J. Davison
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  2. Amir G. Aghdam
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Corresponding author

Correspondence to Edward J. Davison .

Editor information

Editors and Affiliations

  1. Dept. Electrical &, Computer Engineering, Temple University , North 12th Street 1947, Philadelphia, 19122, U.S.A.

    Chang-Hee Won

  2. College of Engineering, Boise State University, University Drive 1910, Boise, 83725-2100, U.S.A.

    Cheryl B. Schrader

  3. Department of Electrical Engineering, University of Notre Dame, Fitzpatrick Hall 275, Notre Dame, 46556-5637, U.S.A.

    Anthony N. Michel

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© 2008 Birkhäuser Boston, a part of Springer Science+Business Media, LLC

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Davison, E.J., Aghdam, A.G. (2008). Characterization and Calculation of Approximate Decentralized Fixed Modes (ADFMs). In: Won, CH., Schrader, C., Michel, A. (eds) Advances in Statistical Control, Algebraic Systems Theory, and Dynamic Systems Characteristics. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4795-7_11

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