DocumentCode :
842107
Title :
Asymptotic unbounded root loci--Formulas and computation
Author :
Sastry, S. Sankar ; Desoer, Charlies A.
Author_Institution :
University of California, Berkley, CA, USA
Volume :
28
Issue :
5
fYear :
1983
fDate :
5/1/1983 12:00:00 AM
Firstpage :
557
Lastpage :
568
Abstract :
We study the asymptotic behavior of the dosed loop eigenvalues (root loci) of a strictly proper linear time-invariant control system as loop gain goes to 
. The formulas are stated in terms of the eigenvalues of nested restricted linear maps of the form 
where S1 and S2 are subspaces of complementary dimension. Additional geometrical insight into the formulas is obtained by mechanizing the formulas using orthogonal projections. Our method and formulas are useful in other asymptotic calculations as well, e.g., hierarchical multiple-time scales aggregation of Markov chains with some infrequent transitions.
. The formulas are stated in terms of the eigenvalues of nested restricted linear maps of the form where SKeywords :
Eigenvalues/eigenvectors; Poles and zeros, linear systems; Control systems; Eigenvalues and eigenfunctions; Feedback loop; Laboratories; Linear systems; Markov processes; Matrix decomposition; NASA; Space technology; Transfer functions;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1983.1103269
Filename :
1103269
Link To Document :
