<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

Fractional descriptor continuous–time linear systems described by the Caputo–Fabrizio derivative

Faculty of Electrical Engineering, Białystok Technical University, Wiejska 45D, 15-351 Białystok,

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The Weierstrass–Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor continuous-time linear systems described by...

Fractional descriptor continuous–time linear systems described by the Caputo–Fabrizio derivative

Published Online: Sep 29, 2016

Page range: 533 - 541

Received: Nov 26, 2015

Accepted: May 25, 2016

DOI: https://doi.org/10.1515/amcs-2016-0037

Keywords
fractional system, descriptor system, continuous-time, linear system, Caputo–Fabrizio derivative

© 2016 Tadeusz Kaczorek et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fractional descriptor continuous–time linear systems described by the Caputo–Fabrizio derivative

Published Online: Sep 29, 2016

Page range: 533 - 541

Received: Nov 26, 2015

Accepted: May 25, 2016

DOI: https://doi.org/10.1515/amcs-2016-0037

Keywordsfractional system, descriptor system, continuous-time, linear system, Caputo–Fabrizio derivative

© 2016 Tadeusz Kaczorek et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
fractional system, descriptor system, continuous-time, linear system, Caputo–Fabrizio derivative