DocumentCode
1362481
Title
Gramian assignment based on the Lyapunov equation
Author
Wicks, Mark A. ; DeCarlo, Raymond A.
Author_Institution
Sch. of Electr. Eng., Purdue Univ., West Lafayette, IN, USA
Volume
35
Issue
4
fYear
1990
fDate
4/1/1990 12:00:00 AM
Firstpage
465
Lastpage
468
Abstract
A theorem on the assignability of the controllability Gramian using state feedback is presented. The approach is based on the Lyapunov equation. Specifically, it shows that the set of Gramian matrices which are assignable using state feedback lies in a vector space and is precisely the intersection of that vector space with the set of positive definite matrices. The results show that it may be possible to reshape the structure of the system indirectly by specifying a desired closed-loop Lyapunov function, rather than by directly assigning eigenvalues or eigenvectors
Keywords
Lyapunov methods; closed loop systems; control system analysis; controllability; eigenvalues and eigenfunctions; feedback; state-space methods; Lyapunov equation; assignability; closed-loop; controllability; eigenvalues; eigenvectors; gramian assignment; state feedback; vector space; Controllability; Covariance matrix; Eigenvalues and eigenfunctions; Ellipsoids; Energy dissipation; Equations; Lyapunov method; State feedback; Stochastic systems; Vectors;
fLanguage
English
Journal_Title
Automatic Control, IEEE Transactions on
Publisher
ieee
ISSN
0018-9286
Type
jour
DOI
10.1109/9.52304
Filename
52304
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