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Positive 2D discrete-time linear Lyapunov systems

100%
Przyborowski P., Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2009
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tom 19
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nr 1
95-105
EN
Two models of positive 2D discrete-time linear Lyapunov systems are introduced. For both the models necessary and sufficient conditions for positivity, asymptotic stability, reachability and observability are established. The discussion is illustrated with numerical examples.
2
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Positivity and stabilization of 2D linear systems

88%
Kaczorek T.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2009
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tom 29
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nr 1
43-52
EN
The problem of finding a gain matrix of the state-feedback of 2D linear system such that the closed-loop system is positive and asymptotically stable is formulated and solved. Necessary and sufficient conditions for the solvability of the problem are established. It is shown that the problem can be reduced to suitable linear programming problem. The proposed approach can be extended to 2D linear system described by the 2D Roesser model.
3
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Positivity and stabilization of fractional 2D linear systems described by the Roesser model

88%
Kaczorek T., Rogowski K.
International Journal of Applied Mathematics and Computer Science
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2010
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tom 20
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nr 1
85-92
EN
A new class of fractional 2D linear discrete-time systems is introduced. The fractional difference definition is applied to each dimension of a 2D Roesser model. Solutions of these systems are derived using a 2D Z-transform. The classical Cayley-Hamilton theorem is extended to 2D fractional systems described by the Roesser model. Necessary and sufficient conditions for the positivity and stabilization by the state-feedback of fractional 2D linear systems are established. A procedure for the computation of a gain matrix is proposed and illustrated by a numerical example.
4
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$L^p$-spaces and quantum dynamical semigroups

63%
Goldstein S., Martin Lindsay J.
Banach Center Publications
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1998
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tom 43
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nr 1
211-216
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