Analysis of the positivity of fractional standard and descriptor continuous-time linear systems by the use of Caputo-Fabrizio definition

Tadeusz Kaczorek

Abstract

Using the Caputo-Fabrizio definition of fractional order derivative the positivity and asymptotic stability of the fractional standard and descriptor continuous-time linear systems are investigated. The solution to the matrix fractional differential state equations is derived. Necessary and sufficient conditions for the positivity and asymptotic stability of the fractional linear systems are established. Tests for checking of the asymptotic stability of the systems are given. The Weierstrass-Kronecker theorem on the decomposition of the regular pencil is extended to the fractional descriptor continuous-time linear systems described by the Caputo-Fabrizio derivative. A method for computing of the solution of the continuous-time systems is presented. Necessary and sufficient conditions for positivity and stability of the descriptor systems are established.