315 research outputs found
Some fundamental properties on the sampling free nabla Laplace transform
Discrete fractional order systems have attracted more and more attention in
recent years. Nabla Laplace transform is an important tool to deal with the
problem of nabla discrete fractional order systems, but there is still much
room for its development. In this paper, 14 lemmas are listed to conclude the
existing properties and 14 theorems are developed to describe the innovative
features. On one hand, these properties make the N-transform more effective and
efficient. On the other hand, they enrich the discrete fractional order system
theor
Description and Realization for a Class of Irrational Transfer Functions
This paper proposes an exact description scheme which is an extension to the
well-established frequency distributed model method for a class of irrational
transfer functions. The method relaxes the constraints on the zero initial
instant by introducing the generalized Laplace transform, which provides a wide
range of applicability. With the discretization of continuous frequency band,
the infinite dimensional equivalent model is approximated by a finite
dimensional one. Finally, a fair comparison to the well-known Charef method is
presented, demonstrating its added value with respect to the state of art.Comment: 9 pages, 9 figure
Analytical calculation of the inverse nabla Laplace transform
The inversion of nabla Laplace transform, corresponding to a causal sequence,
is considered. Two classical methods, i.e., residual calculation method and
partial fraction method are developed to perform the inverse nabla Laplace
transform. For the first method, two alternative formulae are proposed when
adopting the poles inside or outside of the contour, respectively. For the
second method, a table on the transform pairs of those popular functions is
carefully established. Besides illustrating the effectiveness of the developed
methods with two illustrative examples, the applicability are further discussed
in the fractional order case
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