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1
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Fractional positive continuous-time linear systems and their reachability

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
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2008
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tom 18
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nr 2
223-228
EN
A new class of fractional linear continuous-time linear systems described by state equations is introduced. The solution to the state equations is derived using the Laplace transform. Necessary and sufficient conditions are established for the internal and external positivity of fractional systems. Sufficient conditions are given for the reachability of fractional positive systems.
2
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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
|
tom 19
|
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.
3
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Reachability of cone fractional continuous-time linear systems

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2009
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tom 19
|
nr 1
89-93
EN
A new class of cone fractional continuous-time linear systems is introduced. Necessary and sufficient conditions for a fractional linear system to be a cone fractional one are established. Sufficient conditions for the reachability of cone fractional systems are given. The discussion is illustrated with an example of linear cone fractional systems.
4
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Monomial subdigraphs of reachable and controllable positive discrete-time systems

88%
Bru R., Caccetta L., Rumchev V. G.
International Journal of Applied Mathematics and Computer Science
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2005
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tom 15
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nr 1
159-166
EN
A generic structure of reachable and controllable positive linear systems is given in terms of some characteristic components (monomial subdigraphs) of the digraph of a non-negative a pair. The properties of monomial subdigraphs are examined and used to derive reachability and controllability criteria in a digraph form for the general case when the system matrix may contain zero columns. The graph-theoretic nature of these criteria makes them computationally more efficient than their known equivalents. The criteria identify not only the reachability and controllability properties of positive linear systems, but also their reachable and controllable parts (subsystems) when the system does not possess such properties.
5
Content available remote

Analysis of some dual properties in discrete dynamic systems

88%
Zhirabok A.
International Journal of Applied Mathematics and Computer Science
|
2006
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tom 16
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nr 3
297-308
EN
The problem of duality in nonlinear and linear systems is considered. In addition to the known duality between controllability and observability, new dual notions and their properties are investigated. A way to refine these properties through an isomorphic transformation of the original systems is suggested.
6
Content available remote

Controllability and observability of linear discrete-time fractional-order systems

75%
Guermah S., Djennoune S., Bettayeb M.
International Journal of Applied Mathematics and Computer Science
|
2008
|
tom 18
|
nr 2
213-222
EN
In this paper we extend some basic results on the controllability and observability of linear discrete-time fractional-order systems. For both of these fundamental structural properties we establish some new concepts inherent to fractional-order systems and we develop new analytical methods for checking these properties. Numerical examples are presented to illustrate the theoretical results.
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