Investigation, development and application of optimal output feedback theory.
Volume IV,
Measures of eigenvalue/eigenvector sensitivity to system parameters and unmodeled dynamics /
Nesim Halyo.
Description
- Language(s)
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English
- Published
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Washington, D.C. : National Aeronautics and Space Administration, Scientific and Technical Information Division ; 1987.
- Summary
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Some measures of eigenvalue and eigenvector sensitivity applicable to both continuous and discrete linear systems are developed and investigated. An infinite series representation is developed for the eigenvalues and eigenvectors of a system. The coefficients of the series are coupled, but can be obtained recursively using a nonlinear coupled vector difference equation. A new sensitivity measure is developed by considering the effects of unmodeled dynamics. It is shown that the sensitivity is high when any unmodeled eigenvalue is near a modeled eigenvalue. Using a simple example where the sensor dynamics have been neglected, it is shown that high feedback gains produce high eigenvalue/eigenvector sensitivity. The smallest singular value of the return difference is shown not to reflect eigenvalue sensitivity since it increases with the feedback gains. Using an upper bound obtained from the infinite series, a procedure to evaluate whether the sensitivity to parameter variations is within given acceptable bounds is developed and demonstrated by an example.
- Note
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Performing organization report no.: FR-687103.
"NASA CR-4108"--Report documentation page.
"December 1987"--Cover.
Also available online from the NASA Technical Reports Server (http://ntrs.nasa.gov/). Address as of 1/30/06: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19880003587%5f1988003587.pdf.
- Physical Description
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vii, 50 p. :
ill. ;
27 cm.
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University of Illinois at Urbana-Champaign
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