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

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.

Keywords

• fractional system
• descriptor system
• continuous-time
• linear system
• caputo–fabrizio derivative