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Descriptor fractional linear systems with regular pencils

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2013
|
tom 23
|
nr 2
309-315
EN
Methods for finding solutions of the state equations of descriptor fractional discrete-time and continuous-time linear systems with regular pencils are proposed. The derivation of the solution formulas is based on the application of the Z transform, the Laplace transform and the convolution theorems. Procedures for computation of the transition matrices are proposed. The efficiency of the proposed methods is demonstrated on simple numerical examples.
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Simple conditions for practical stability of positive fractional discrete-time linear systems

75%
Busłowicz M., Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2009
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tom 19
|
nr 2
263-269
EN
In the paper the problem of practical stability of linear positive discrete-time systems of fractional order is addressed. New simple necessary and sufficient conditions for practical stability and for practical stability independent of the length of practical implementation are established. It is shown that practical stability of the system is equivalent to asymptotic stability of the corresponding standard positive discrete-time systems of the same order. The discussion is illustrated with numerical examples.
3
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Positive stable realizations of fractional continuous-time linear systems

75%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2011
|
tom 21
|
nr 4
697-702
EN
Conditions for the existence of positive stable realizations with system Metzler matrices for fractional continuous-time linear systems are established. A procedure based on the Gilbert method for computation of positive stable realizations of proper transfer matrices is proposed. It is shown that linear minimum-phase systems with real negative poles and zeros always have positive stable realizations.
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