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Abstract

In the paper positive fractional continuous-time linear systems are considered. Positive fractional systems without delays and positive fractional systems with a single delay in control are studied. New criteria for approximate and exact controllability of systems without delays as well as a relative controllability criterion of systems with delay are established and proved. Numerical examples are presented for different controllability criteria. A practical application is proposed.
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Bibliography

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Authors and Affiliations

Beata Sikora
1
ORCID: ORCID
Nikola Matlok
1

  1. Department of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland
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Abstract

The paper investigates the controllability of fractional descriptor linear systems with constant delays in control. The Caputo fractional derivative is considered. Using the Drazin inverse and the Laplace transform, a formula for solving of the matrix state equation is obtained. New criteria of relative controllability for Caputo’s fractional descriptor systems are formulated and proved. Both constrained and unconstrained controls are considered. To emphasize the importance of the theoretical studies, an application to electrical circuits is presented as a practical example.
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Authors and Affiliations

Beata Sikora
ORCID: ORCID

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Abstract

This paper focuses on the global practical Mittag-Leffler feedback stabilization problem for a class of uncertain fractional-order systems. This class of systems is a larger class of nonlinearities than the Lipschitz ones. Based on the quasi-one-sided Lipschitz condition, firstly, we provide sufficient conditions for the practical observer design. Then, we exhibit that practical Mittag-Leffler stability of the closed loop system with a linear, state feedback is attained. Finally, a separation principle is established and we prove that the closed loop system is practical Mittag-Leffler stable.
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Authors and Affiliations

Imed Basdouri
1
ORCID: ORCID
Souad Kasmi
2
Jean Lerbet
3

  1. Gafsa University, Faculty of Sciences of Gafsa, Department of Mathematics, Zarroug Gafsa 2112 Tunisia
  2. Sfax University, Faculty of Sciences of Sfax, Department of Mathematics, BP 1171 Sfax 3000 Tunisia
  3. Laboratoire de Mathématiques et de Modélisation d’Evry, Univ d’Evry, Université Paris Saclay, France

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