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Positivity and stability of fractional descriptor time-varying discrete-time linear systems

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2016
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tom 26
|
nr 1
5-13
EN
The Weierstrass-Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor timevarying discrete-time linear systems. A method for computing solutions of fractional systems is proposed. Necessary and sufficient conditions for the positivity of these systems are established.
2
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Realization problem for positive multivariable discretetime linear systems with delays in the state vector and inputs

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2006
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tom 16
|
nr 2
169-174
EN
The realization problem for positive multivariable discrete-time systems with delays in the state and inputs is formulated and solved. Conditions for its solvability and the existence of a minimal positive realization are established. A procedure for the computation of a positive realization of a proper rational matrix is presented and illustrated with examples.
3
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Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2013
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tom 23
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nr 1
29-33
EN
The Drazin inverse of matrices is applied to find the solutions of the state equations of descriptor fractional discrete-time systems with regular pencils. An equality defining the set of admissible initial conditions for given inputs is derived. The proposed method is illustrated by a numerical example.
4
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Minimal realization for positive multivariable linear systems with delay

100%
Kaczorek T., Busłowicz M.
International Journal of Applied Mathematics and Computer Science
|
2004
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tom 14
|
nr 2
181-187
EN
The realization problem for positive multivariable discrete-time systems with one time delay is formulated and solved. Conditions for the solvability of the realization problem are established. A procedure for the computation of a minimal positive realization of a proper rational matrix is presented and illustrated by an example.
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