دانلود SINGULAR FRACTIONAL CONTINUOUS-TIME AND DISCRETE-TIME LINEAR SYSTEMS

Abstract

New classes of singular fractional continuous-time and discrete-time linear systems are introduced. Electrical circuits are example  of  singular  fractional  continuous-time  systems.  Using  the  Caputo  definition  of  the  fractional  derivative,  the  Weierstrass  regular  pencil decomposition  and  Laplace  transformation  the  solution  to  the  state  equation  of  singular  fractional  linear  systems  is  derived.  It  is  shown that every electrical circuit is a singular fractional systems if it contains at least one mesh consisting of branches with only i deal supercon-densators  and  voltage  sources  or  at  least  one    node  with  branches  with  supercoils.  Using  the  Weierstrass  regular  pencil  decomposition the solution to the state equation of singular fractional discrete-time linear systems is derived. The considerations are illustrated by numerical examples.