Modeling of open-loop stable linear systems using a combination of a finite fractional derivative and orthonormal basis functions

Abstract

This paper presents new results in modeling of linear open-loop stable systems by means of discrete-time finite fractional orthonormal basis functions, in particular the Laguerre functions. New stability conditions are offered and a useful modification to finite fractional derivative is introduced, called normalized finite fractional derivative. Simulation examples illustrate the usefulness of the new modeling methodology.