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A quadratic optimal control problem for a class of linear discrete distributed systems

100%
Rachik M., Lhous M., Kahlaoui O. E.
International Journal of Applied Mathematics and Computer Science
|
2006
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tom 16
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nr 4
431-440
EN
A linear quadratic optimal control problem for a class of discrete distributed systems is analyzed. To solve this problem, we introduce an adequate topology and establish that optimal control can be determined though an inversion of the appropriate isomorphism. An example and a numerical approach are given.
2
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Fractional descriptor continuous-time linear systems described by the Caputo-Fabrizio derivative

88%
Kaczorek T., Borawski K.
International Journal of Applied Mathematics and Computer Science
|
2016
|
tom 26
|
nr 3
533-541
EN
The Weierstrass-Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor continuous-time linear systems described by the Caputo-Fabrizio derivative. A method for computing solutions of continuous-time systems is presented. Necessary and sufficient conditions for the positivity and stability of these systems are established. The discussion is illustrated with a numerical example.
3
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Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils

88%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2013
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tom 23
|
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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Extension of the Cayley-Hamilton theorem to continuous-time linear systems with delays

88%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2005
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tom 15
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nr 2
231-234
EN
The classical Cayley-Hamilton theorem is extended to continuous-time linear systems with delays. The matrices of the system with delays satisfy algebraic matrix equations with coefficients of the characteristic polynomial.
5
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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.
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