Extended Transfer-Function and Pole-Zero Cancellation in Linear Time-Varying Systems
Pole-zero cancellation is a well-known and important concept in linear time-invariant systems. In contrast, transfer functions as well as poles and zeros are not defined for linear time-varying systems. In this paper, we attempt to generalize the concept of pole-zero cancellation to linear time-vary...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2019-09-01
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| Series: | SICE Journal of Control, Measurement, and System Integration |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.9746/jcmsi.12.209 |
| _version_ | 1797661051958853632 |
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| author | Ichiro Jikuya Shingo Kondo |
| author_facet | Ichiro Jikuya Shingo Kondo |
| author_sort | Ichiro Jikuya |
| collection | DOAJ |
| description | Pole-zero cancellation is a well-known and important concept in linear time-invariant systems. In contrast, transfer functions as well as poles and zeros are not defined for linear time-varying systems. In this paper, we attempt to generalize the concept of pole-zero cancellation to linear time-varying systems. We first introduce the new concept of extended transfer-function for linear time-varying systems in the time domain instead of the frequency domain. We then propose the computational procedure of pole-zero cancellation to linear time-varying systems. We finally discuss the meaning of the proposed computational procedure regardless of the lack of poles and zeros in linear time-varying systems. The proposed concept and computational procedure are illustrated by a numerical example. |
| first_indexed | 2024-03-11T18:38:41Z |
| format | Article |
| id | doaj.art-55b8b78a27874d46960bba5cc05adbf1 |
| institution | Directory Open Access Journal |
| issn | 1884-9970 |
| language | English |
| last_indexed | 2024-03-11T18:38:41Z |
| publishDate | 2019-09-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | SICE Journal of Control, Measurement, and System Integration |
| spelling | doaj.art-55b8b78a27874d46960bba5cc05adbf12023-10-12T13:43:55ZengTaylor & Francis GroupSICE Journal of Control, Measurement, and System Integration1884-99702019-09-0112520921410.9746/jcmsi.12.20912103272Extended Transfer-Function and Pole-Zero Cancellation in Linear Time-Varying SystemsIchiro Jikuya0Shingo Kondo1Graduate School of Natural Science and Technology, Kanazawa UniversityGraduate School of Natural Science and Technology, Kanazawa UniversityPole-zero cancellation is a well-known and important concept in linear time-invariant systems. In contrast, transfer functions as well as poles and zeros are not defined for linear time-varying systems. In this paper, we attempt to generalize the concept of pole-zero cancellation to linear time-varying systems. We first introduce the new concept of extended transfer-function for linear time-varying systems in the time domain instead of the frequency domain. We then propose the computational procedure of pole-zero cancellation to linear time-varying systems. We finally discuss the meaning of the proposed computational procedure regardless of the lack of poles and zeros in linear time-varying systems. The proposed concept and computational procedure are illustrated by a numerical example.http://dx.doi.org/10.9746/jcmsi.12.209pole-zero cancellationlinear time-varying systemkalman canonical decompositionminimal realizationcompanion form |
| spellingShingle | Ichiro Jikuya Shingo Kondo Extended Transfer-Function and Pole-Zero Cancellation in Linear Time-Varying Systems SICE Journal of Control, Measurement, and System Integration pole-zero cancellation linear time-varying system kalman canonical decomposition minimal realization companion form |
| title | Extended Transfer-Function and Pole-Zero Cancellation in Linear Time-Varying Systems |
| title_full | Extended Transfer-Function and Pole-Zero Cancellation in Linear Time-Varying Systems |
| title_fullStr | Extended Transfer-Function and Pole-Zero Cancellation in Linear Time-Varying Systems |
| title_full_unstemmed | Extended Transfer-Function and Pole-Zero Cancellation in Linear Time-Varying Systems |
| title_short | Extended Transfer-Function and Pole-Zero Cancellation in Linear Time-Varying Systems |
| title_sort | extended transfer function and pole zero cancellation in linear time varying systems |
| topic | pole-zero cancellation linear time-varying system kalman canonical decomposition minimal realization companion form |
| url | http://dx.doi.org/10.9746/jcmsi.12.209 |
| work_keys_str_mv | AT ichirojikuya extendedtransferfunctionandpolezerocancellationinlineartimevaryingsystems AT shingokondo extendedtransferfunctionandpolezerocancellationinlineartimevaryingsystems |