TY - JOUR
T1 - The operator Carleson measure criterion for admissibility of control operators for diagonal semigroups on l2
AU - Hansen, Scott
AU - Weiss, George
N1 - Funding Information:
All vector spaces considered here are complex. We represent elements of l 2 as infinite column matrices (i.e., matrices consisting of a single col- * Supported in part by the Air Force Office of Scientific Research under contract AFOSR-89-0268. * * Supported mainly by the Weizraarm Fellowship, and also by the Air Force Office of Scientific Research under con-tract AFOSR-89-0031.
PY - 1991/3
Y1 - 1991/3
N2 - Suppose a control system is described by a diagonal semigroup on the state space l2 and by an unbounded control operator B defined on the input space l2. We formulate a condition called the operator Carleson measure criterion, and show that this condition is necessary for the admissibility of B. If the semigroup is analytic or invertible, then the condition is sufficient as well. Our results extend the ones of Ho, Russell and Weiss concerning the case where the input space is one dimensional.
AB - Suppose a control system is described by a diagonal semigroup on the state space l2 and by an unbounded control operator B defined on the input space l2. We formulate a condition called the operator Carleson measure criterion, and show that this condition is necessary for the admissibility of B. If the semigroup is analytic or invertible, then the condition is sufficient as well. Our results extend the ones of Ho, Russell and Weiss concerning the case where the input space is one dimensional.
KW - Admissible control operators
KW - operator Carleson measures
UR - http://www.scopus.com/inward/record.url?scp=0026120763&partnerID=8YFLogxK
U2 - 10.1016/0167-6911(91)90051-F
DO - 10.1016/0167-6911(91)90051-F
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AN - SCOPUS:0026120763
SN - 0167-6911
VL - 16
SP - 219
EP - 227
JO - Systems and Control Letters
JF - Systems and Control Letters
IS - 3
ER -