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
Link To Document :
