On the state space and frequency domain characterization of H∞-norm of sampled-data systems

1993 ◽  
Vol 21 (2) ◽  
pp. 163-172 ◽  
Author(s):  
Yutaka Yamamoto
Keyword(s):  
State Space ◽  
Frequency Domain ◽  
The State ◽  
Data Systems ◽  
Sampled Data

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.

Stability analysis for complicated sampled-data systems via descriptor remodelling

2018 ◽  
Vol 36 (4) ◽  
pp. 1347-1373 ◽  
Author(s):  
Jun Zhou ◽  
Ketian Gao ◽  
Xinbiao Lu
Keyword(s):  
Stability Analysis ◽  
Frequency Domain ◽  
Continuous Time ◽  
Transfer Functions ◽  
Open Loop ◽  
Spectral Features ◽  
Data Systems ◽  
Sampled Data ◽  
Digital Controllers ◽  
Lifting Technique

AbstractA new stability analysis technique is developed in this paper for complicated sampled-data systems with both analogue and digital controllers, by frequency-domain equivalence in the continuous-time sense and time-delayed descriptor (or singular) state-space realization remodelling. The technique is independent of the lifting technique and thus employs neither structural nor spectral features of any discrete-time transfer functions of continuous-time plants. The suggested criteria are stated with frequency-domain conditions, involving neither open-loop unstable poles nor contour/locus-orientation-related encirclements counting. The criteria are implementable graphically with locus plotting or numerically tractable without locus plotting. The descriptor remodelling advantages are further exploited in surmounting infinite dimensionality and structural/spectral features unavailability in multi-rate and time-delayed sampled-data systems. Numerical examples are included to illustrate the main results.

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