Milang Journal of Mathematics and Its Applications
Vol. 12 No. 2 (2013): Journal of Mathematics and Its Applications

MOBIUS AND DELTA TRANSFORMS IN THE UNIFICATION OF CONTINUOUS-DISCRETE SPACES

T. BAKHTIAR (Bogor Agricultural University)
S. SAMSURIZAL (Bogor Agricultural University)
N. ALIATININGTYAS (Bogor Agricultural University)

Article Info

Publish Date
01 Dec 2013

Abstract

It is well-known that in control theory the stability region of continuous- time system is laid in the left half plane of complex space, while that of discrete-time system is dwelled inside a unit circle. The former fact might be shown by exploiting the Laplace transform and the later by utilizing the corresponding zeta transform. In this paper we revealed the connectivity of both regions by employing M¨obius transform. We also used the same transform to derive continuous/discrete-time counterpart of several existing results, including Bode integral and Poisson-Jensen formula. We then demonstrated their unification property by using delta transform. Some numerical examples were provided to verify our results.

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Journal Info
Milang Journal of Mathematics and Its Applications
Website

Abbrev

jmap

Publisher

Institut Pertanian Bogor

Subject

Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Earth & Planetary Sciences Mathematics

Description

The name MILANG is a Sundanese word that means “to count”, and is also an acronym of the topics covered in the journal: Mathematics in Informatics, Life Sciences, Actuarial Science, Natural Sciences, and Graph ...