Characterization of Non-reachable States in Irreversible CA State Space

2008 ◽  
pp. 160-167 ◽  
Author(s):  
Sukanta Das ◽  
Biplab K. Sikdar
Keyword(s):  
State Space

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

scholarly journals On Bumps and Reduction of Switching Transients in Multicontroller Systems

2007 ◽  
Vol 2007 ◽  
pp. 1-17 ◽  
Author(s):  
Joseph J. Yamé ◽  
Michel Kinnaert
Keyword(s):  
State Space ◽  
Closed Loop ◽  
Open Loop ◽  
Space Representation ◽  
Control Loop ◽  
Minimal State ◽  
State Space Representation ◽  
Common Memory ◽  
Linear Controllers

This paper is concerned with the realization and implementation of multicontroller systems, consisting of several linear controllers, subject to the bump phenomenon which occurs when switching between one controller acting in closed loop and another controller in the set of “offline” controllers waiting to take over the control loop. Based on a deep characterization of the bump phenomenon, the paper gives a novel and simple parameterization of such set of linear controllers, possibly having different state dimensions, to cope with bumps and their undesirable transients in switched-mode systems. The proposed technique is based on a non minimal state-space representation allowing a common memory and a unique dynamics shared by all controllers in that set. It also makes each initially open-loop unstable controller run in a stable way regardless of whether that controller is connected to the controlled process.

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