Cayley–Hamilton theorem for fractional linear systems

Abstract

The classical Cayley–Hamilton theorem is extended to fractional continuous-time and discrete-time linear systems. It is shown that theMittag-Leffler functions of the fractional continuous-time linear system and the Φi matrices of the fractional discrete-time linear systems satisfy their characteristic equations. The extensions are based on the application of the Lagrange–Sylvester formula of functions of matrices.