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1
Content available remote Reachability, controllability to zero and observability of the positive discrete-time Lyapunov systems
Kaczorek T., Przyborowski P.
Control and Cybernetics
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2009
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Vol. 38, no 2
529-541
EN
The new necessary and sufficient conditions for the reachability, controllability to zero and observability of the positive discrete-time Lyapunov systems are established. The notion of the dual positive Lyapunov system is introduced and the relationship between the reachability and observability are given. The considerations are illustrated with numerical examples.
2
Content available remote Fractional discrete-time Lyapunov cone-systems
Przyborowski P.
Przegląd Elektrotechniczny
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2008
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R. 84, nr 5
47-52
EN
The fractional discrete-time Lyapunov cone-systems are introduced. The necessary and sufficient conditions for being the cone system, reachability, controllability to zero and observability of the systems are established. The sufficient conditions for stability are given. The notion of the dual fractional Lyapunov cone-system is introduced and the relationship between the reachability and observability is given. The considerations are illustrated on the numerical example.
PL
Praca przedstawia stożkowe dyskretne układy Lapunowa ułamkowego rzędu. Ustanowione są warunki konieczne i wystarczające bycia układem stożkowym, osiągalności, sterowalności do zera i obserwowalności dla tego typu układów. Przedstawione są również układy dualne do stożkowych dyskretnych układów Lapunowa ułamkowego rzędu oraz związek między osiągalnością i obserwowalnością. Rozważania są zilustrowane na przykładach numerycznych.
3
Content available Reachability and controllability of positive fractional discrete-time systems with delay
Trzasko W.
Journal of Automation Mobile Robotics and Intelligent Systems
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2008
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Vol. 2, No. 3
43-47
EN
In the paper the positive fractional discrete-time linear systems with delay described by the state equations are considered. The solution to the state equations is derived using the Z transform. Necessary and sufficient conditions are established for the positivity, reachability and controllability to zero for fractional systems with one delay in state. The considerations are illustrated by an example.
4
Content available Fractional 2D linear systems
Kaczorek T.
Journal of Automation Mobile Robotics and Intelligent Systems
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2008
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Vol. 2, No. 2
5-9
5
Content available remote Positive fractional discrete-time Lyapunov systems
Przyborowski P.
Archives of Control Sciences
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2008
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Vol. 18, no. 1
121-134
EN
The positive linear fractional discrete-time Lyapunov systems are introduced. The necessary and sufficient conditions for the positivity, reachability, controllability to zero and observability of the systems are established. The sufficient conditions for stability are given. The notion of the dual positive fractional Lyapunov system is introduced and the relationship between the reachability and observability is given. The considerations are illustrated on the numerical example.
6
Content available remote Reachability and controllability to zero of cone fractional linear systems
Kaczorek T.
Archives of Control Sciences
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2007
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Vol. 17, no. 4
357-367
EN
A new class of cone fractional linear discrete-time systems is introduced. Necessary and sufficient conditions for the reachability and controllability to zero of the cone fractional systems are established.
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