State-space characterization of all solutions to positive real control problem

1997 ◽  
Author(s):  
Chee-Fai Yung
Keyword(s):  
Control Problem ◽  
State Space ◽  
Positive Real ◽  
All Solutions ◽  
Space Characterization

THE BANACH-LIE *-ALGEBRA OF MULTIPLICATION OPERATORS ON A W*-ALGEBRA

2011 ◽  
Vol 04 (02) ◽  
pp. 235-261
Author(s):  
Maysaa Alqurashi ◽  
Najla A. Altwaijry ◽  
C. Martin Edwards ◽  
Christopher S. Hoskin
Keyword(s):  
State Space ◽  
Lie Algebra ◽  
The State ◽  
Multiplication Operators ◽  
Dual Cone ◽  
Positive Real ◽  
Linear Isometry ◽  
Real Linear ◽  
Special Case

The hermitian part [Formula: see text] of the Banach-Lie *-algebra [Formula: see text] of multiplication operators on the W *-algebra A is a unital GM-space, the base of the dual cone in the dual GL-space [Formula: see text] of which is affine isomorphic and weak*-homeomorphic to the state space of [Formula: see text]. It is shown that there exists a Lie *-isomorphism ϕ from the quotient (A ⊕∞ Aop)/K of an enveloping W *-algebra A ⊕∞ Aop of A by a weak*-closed Lie *-ideal K onto [Formula: see text], the restriction to the hermitian part ((A ⊕∞ Aop)/K)h of which is a bi-positive real linear isometry, thereby giving a characterization of the state space of [Formula: see text]. In the special case in which A is a W *-factor this leads to a further identification of the state space of [Formula: see text] in terms of the state space of A. For any W *-algebra A, the Banach-Lie *-algebra [Formula: see text] coincides with the set of generalized derivations of A, and, as an application, a formula is obtained for the norm of an element of [Formula: see text] in terms of a centre-valued 'norm' on A, which is similar to that previously obtained by non-order-theoretic methods.

scholarly journals State Space Characterization of Disjunctive Single-Unit Resource Allocation Systems

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 51515-51527
Author(s):  
Oussama Karoui ◽  
Mohamed Khalgui ◽  
Yufeng Chen ◽  
Naiqi Wu ◽  
Ateekh-Ur Rehman ◽  
...  
Keyword(s):  
Resource Allocation ◽  
State Space ◽  
Single Unit ◽  
Resource Allocation Systems ◽  
Space Characterization
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