Fractional-Order Discrete-Time Laguerre Filters: A New Tool for Modeling and Stability Analysis of Fractional-Order LTI SISO Systems

Abstract

This paper presents new results on modeling and analysis of dynamics of fractional-order discrete-time linear time-invariant single-input single-output (LTI SISO) systems by means of new, two-layer, “fractional-order discrete-time Laguerre filters.” It is interesting that the fractionality of the filters at the upper system dynamics layer is directly projected from the lower Laguerre-based approximation layer for the Grünwald-Letnikov difference. A new stability criterion for discrete-time fractional-order Laguerre-based LTI SISO systems is introduced and supplemented with a stability preservation analysis. Both the stability criterion and the stability preservation analysis bring up rather surprising results, which is illustrated with simulation examples.