DocumentCode
796862
Title
On the existence of optimal solutions for the linear system quadratic cost problem
Author
Sivan, Raphael ; Shalvi, Shlomo
Author_Institution
Tenchion--Israel Institute of Technology, Haifa, Israel
Volume
13
Issue
2
fYear
1968
fDate
4/1/1968 12:00:00 AM
Firstpage
188
Lastpage
191
Abstract
The linear system 
with the quadratic cost function 
is considered. The following equivalent conditions are shown to be necessary and sufficient for the existence of a solution to the optimization problem: 1) the existence of a positive definite solution for the algebraic matrix Riccati equation; 2) the existence of a vector 
such that the matrix 
is asymptotically stables and 3) the cancellations in the vector 
are only of stable factors.
with the quadratic cost function is considered. The following equivalent conditions are shown to be necessary and sufficient for the existence of a solution to the optimization problem: 1) the existence of a positive definite solution for the algebraic matrix Riccati equation; 2) the existence of a vector such that the matrix is asymptotically stables and 3) the cancellations in the vector are only of stable factors.Keywords
Linear systems, time-invariant continuous-time; Optimal control; Boundary conditions; Control systems; Cost function; Gas detectors; Linear systems; Open loop systems; Optimal control; Signal design; Stochastic resonance; Stochastic systems;
fLanguage
English
Journal_Title
Automatic Control, IEEE Transactions on
Publisher
ieee
ISSN
0018-9286
Type
jour
DOI
10.1109/TAC.1968.1098845
Filename
1098845
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