TY - GEN
T1 - Perturbation analysis of eigenvalues of a class of self-adjoint operators
AU - Moarref, Rashad
AU - Fardad, Makan
AU - Jovanović, Mihailo R.
PY - 2008
Y1 - 2008
N2 - 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.
AB - 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.
KW - Perturbation analysis
KW - Spatially periodic systems
KW - Transient response
UR - http://www.scopus.com/inward/record.url?scp=52449100729&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=52449100729&partnerID=8YFLogxK
U2 - 10.1109/ACC.2008.4586615
DO - 10.1109/ACC.2008.4586615
M3 - Conference contribution
AN - SCOPUS:52449100729
SN - 9781424420797
T3 - Proceedings of the American Control Conference
SP - 955
EP - 960
BT - 2008 American Control Conference, ACC
T2 - 2008 American Control Conference, ACC
Y2 - 11 June 2008 through 13 June 2008
ER -