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Independence of asymptotic stability of positive 2D linear systems with delays of their delays

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2009
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tom 19
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nr 2
255-261
EN
It is shown that the asymptotic stability of positive 2D linear systems with delays is independent of the number and values of the delays and it depends only on the sum of the system matrices, and that the checking of the asymptotic stability of positive 2D linear systems with delays can be reduced to testing that of the corresponding positive 1D systems without delays. The effectiveness of the proposed approaches is demonstrated on numerical examples.
2
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Fractional positive continuous-time linear systems and their reachability

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2008
|
tom 18
|
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.
3
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Minimum energy control of fractional positive continuous-time linear systems with bounded inputs

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2014
|
tom 24
|
nr 2
335-340
EN
A minimum energy control problem for fractional positive continuous-time linear systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of a solution to the problem are established. A procedure for solving the problem is proposed and illustrated with a numerical example.
4
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New stability conditions for positive continuous-discrete 2D linear systems

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2011
|
tom 21
|
nr 3
521-524
EN
New necessary and sufficient conditions for asymptotic stability of positive continuous-discrete 2D linear systems are established. Necessary conditions for the stability are also given. The stability tests are demonstrated on numerical examples.
5
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Positive partial realization problem for linear discrete-time systems

75%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2007
|
tom 17
|
nr 2
165-171
EN
A partial realization problem for positive linear discrete-time systems is addressed. Sufficient conditions for the existence of its solution are established. A procedure for the computation of a positive partial realization for a given finite sequence of the values of the impulse response is proposed. The procedure is illustrated by four numerical examples.
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