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This paper presents a general, modified framework for various time-domain approximations to the Grünwald-Letnikov fractional difference, namely finite fractional and Laguerre-based differences. The approximations are applied in the modeling problem for linear fractional-order state space systems, with two different implementation schemes presented.
This paper presents new results in the reduction of a steady-state error in modeling of the Grünwald-Letnikov (GL) discrete-time fractional difference by means of discrete-time Laguerre filters. A discussion of various approximation criteria contributes to the steady-state accuracy problem. The paper is culminated with the presentation of finite fractional/Laguerre-based difference (FFLD), whose excellent...
This paper presents a new concept of modeling of LTI SISO discrete-time fractional-order systems, in which the Laguerre filters are employed to model both 1) the Grünwald-Letnikov fractional difference and 2) a dynamics of the LTI SISO fractional-order system. Such a ‘double-Laguerre’ concept yields original accuracy and computational results at both modeling stages, illustrated with a series of simulation...
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