Investigation, development and application of optimal output feedback theory. Volume IV, Measures of eigenvalue/eigenvector sensitivity to system parameters and unmodeled dynamics

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100 1 ‡aHalyo, Nesim.
245 1 0 ‡aInvestigation, development and application of optimal output feedback theory. ‡nVolume IV, ‡pMeasures of eigenvalue/eigenvector sensitivity to system parameters and unmodeled dynamics / ‡cNesim Halyo.
260 ‡aWashington, D.C. : ‡bNational Aeronautics and Space Administration, Scientific and Technical Information Division ; ‡aSpringfield, Va. : ‡bFor sale by the National Technical Information Service [distributor], ‡c1987.
300 ‡avii, 50 p. : ‡bill. ; ‡c27 cm.
490 0 ‡aNASA contractor report ; ‡v4108
500 ‡aPerforming organization report no.: FR-687103.
500 ‡a"NASA CR-4108"--Report documentation page.
500 ‡a"December 1987"--Cover.
504 ‡aIncludes bibliographical references (p. 43-45).
520 ‡aSome 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.
530 ‡aAlso 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.
536 ‡aPerformed by Information & Control Systems, Inc., Hampton, VA for Langley Research Center ‡bNAS1-15759; ‡h505-66-41-04
538 ‡aMode of access: Internet.
650 7 ‡aVectors (mathematics). ‡2nasat
650 7 ‡aRobustness (mathematics). ‡2nasat
650 7 ‡aNonlinear equations. ‡2nasat
650 7 ‡aLinear systems. ‡2nasat
650 7 ‡aDynamical systems. ‡2nasat
650 7 ‡aCoupled modes. ‡2nasat
650 7 ‡aSystems analysis. ‡2nasat
650 7 ‡aSensitivity. ‡2nasat
650 7 ‡aOptimization. ‡2nasat
650 7 ‡aIndependent variables. ‡2nasat
650 7 ‡aFeedback. ‡2nasat
650 7 ‡aEigenvectors. ‡2nasat
650 7 ‡aEigenvalues. ‡2nasat
710 2 ‡aLangley Research Center.
710 2 ‡aInformation & Control Systems, inc.
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