Perturbation analysis of eigenvalues of a class of self-adjoint operators

Rashad Moarref, Makan Fardad, Mihailo R. Jovanović

Research output: Chapter in Book/Entry/PoemConference contribution


We consider a class of spatially invariant systems whose coefficients are perturbed by spatially periodic functions. We analyze changes in transient behavior under the effect of such perturbations. This is done by performing a spectral analysis of the state transition operator at every point in time. Computational complexity is significantly reduced by using a procedure that captures the influence of the perturbation on only the largest singular values of the state transition operator. Furthermore, we show that the problem of computing corrections of all orders to the maximum singular values collapses to that of finding the eigenvalues of a set of finite dimensional matrices. Finally, we demonstrate the predictive power of this method via an example.

Original languageEnglish (US)
Title of host publication2008 American Control Conference, ACC
Number of pages6
StatePublished - Sep 30 2008
Externally publishedYes
Event2008 American Control Conference, ACC - Seattle, WA, United States
Duration: Jun 11 2008Jun 13 2008

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Other2008 American Control Conference, ACC
Country/TerritoryUnited States
CitySeattle, WA


  • Perturbation analysis
  • Spatially periodic systems
  • Transient response

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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