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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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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.
3
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Optimal approximation simulation and analog realization of the fundamental fractional order transfer function

100%
Djouambi A., Charef A., Besancon A. V.
International Journal of Applied Mathematics and Computer Science
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2007
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tom 17
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nr 4
455-462
EN
This paper provides an optimal approximation of the fundamental linear fractional order transfer function using a distribution of the relaxation time function. Simple methods, useful in systems and control theories, which can be used to approximate the irrational transfer function of a class of fractional systems fora given frequency band by a rational function are presented. The optimal parameters of the approximated model are obtained by minimizing simultaneously the gain and the phase error between the irrational transfer function and its rational approximation. A simple analog circuit, which can serve as a fundamental analog fractional system is obtained. Illustrative examples are presented to show the quality and usefulness of the approximation method.
4
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Positivity and stabilization of fractional 2D linear systems described by the Roesser model

88%
Kaczorek T., Rogowski K.
International Journal of Applied Mathematics and Computer Science
|
2010
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tom 20
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nr 1
85-92
EN
A new class of fractional 2D linear discrete-time systems is introduced. The fractional difference definition is applied to each dimension of a 2D Roesser model. Solutions of these systems are derived using a 2D Z-transform. The classical Cayley-Hamilton theorem is extended to 2D fractional systems described by the Roesser model. Necessary and sufficient conditions for the positivity and stabilization by the state-feedback of fractional 2D linear systems are established. A procedure for the computation of a gain matrix is proposed and illustrated by a numerical example.
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