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Descriptor fractional 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 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.
2
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Reduced-order fractional descriptor observers for a class of fractional descriptor continuous-time nonlinear systems

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2016
|
tom 26
|
nr 2
277-283
EN
Fractional descriptor reduced-order nonlinear observers for a class of fractional descriptor continuous-time nonlinear systems are proposed. Sufficient conditions for the existence of the observers are established. The design procedure for the observers is given and demonstrated on a numerical example.
3
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Minimum energy control of descriptor fractional discrete-time linear systems with two different fractional orders

100%
Sajewski Ł.
International Journal of Applied Mathematics and Computer Science
|
2017
|
tom 27
|
nr 1
33-41
EN
Reachability and minimum energy control of descriptor fractional discrete-time linear systems with different fractional orders are addressed. Using the Weierstrass-Kronecker decomposition theorem of the regular pencil, a solution to the state equation of descriptor fractional discrete-time linear systems with different fractional orders is given. The reachability condition of this class of systems is presented and used for solving the minimum energy control problem. The discussion is illustrated with numerical examples.
4
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Minimum energy control of fractional descriptor positive discrete-time linear systems

100%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2014
|
tom 24
|
nr 4
735-743
EN
Necessary and sufficient conditions for the positivity and reachability of fractional descriptor positive discrete-time linear systems are established. The minimum energy control problem for descriptor positive systems is formulated and solved. Sufficient conditions for the existence of a solution to the minimum energy control problem are given. A procedure for computation of optimal input sequences and a minimal value of the performance index is proposed and illustrated by a numerical example.
5
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Pointwise completeness and pointwise degeneracy of positive fractional descriptor continuous-time linear systems with regular pencils

88%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2015
|
tom 25
|
nr 2
217-221
EN
Pointwise completeness and pointwise degeneracy of positive fractional descriptor continuous-time linear systems with regular pencils are addressed. Conditions for pointwise completeness and pointwise degeneracy of the systems are established and illustrated by an example.
6
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Positivity and stability of fractional descriptor time-varying discrete-time linear systems

88%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2016
|
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.
7
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Robust sensor fault estimation for descriptor-LPV systems with unmeasurable gain scheduling functions: application to an anaerobic bioreactor

88%
López-Estrada F.-R., Ponsart J.-C., Theilliol D., Astorga-Zaragoza C.-M., Camas-Anzueto J.-L.
International Journal of Applied Mathematics and Computer Science
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2015
|
tom 25
|
nr 2
233-244
EN
This paper addresses the design of a state estimation and sensor fault detection, isolation and fault estimation observer for descriptor-linear parameter varying (D-LPV) systems. In contrast to where the scheduling functions depend on some measurable time varying state, the proposed method considers the scheduling function depending on an unmeasurable state vector. In order to isolate, detect and estimate sensor faults, an augmented system is constructed by considering faults to be auxiliary state vectors. An unknown input LPV observer is designed to estimate simultaneously system states and faults. Sufficient conditions to guarantee stability and robustness against the uncertainty provided by the unmeasurable scheduling functions and the influence of disturbances are synthesized via a linear matrix inequality (LMI) formulation by considering H∞ and Lyapunov approaches. The performances of the proposed method are illustrated through the application to an anaerobic bioreactor model.
8
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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.
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