Symmetric Properties of Routh–Hurwitz and Schur–Cohn Stability Criteria
It is often noticed in the literature that some key results on the stability of discrete-time systems of difference equations are obtained from their corresponding results on the stability of continuous-time systems of differential equations using suitable conformal mappings or bilinear transformati...
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| Format: | Article |
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MDPI AG
2022-03-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/3/603 |
| _version_ | 1797441509911429120 |
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| author | Ziad Zahreddine |
| author_facet | Ziad Zahreddine |
| author_sort | Ziad Zahreddine |
| collection | DOAJ |
| description | It is often noticed in the literature that some key results on the stability of discrete-time systems of difference equations are obtained from their corresponding results on the stability of continuous-time systems of differential equations using suitable conformal mappings or bilinear transformations. Such observations lead to the search for a unified approach to the study of root distribution for real and complex polynomials, with respect to the left-half plane for continuous-time systems (Routh–Hurwitz stability) and with respect to the unit disc for discrete-time systems (Schur–Cohn stability). This paper is a further contribution toward this objective. We present, in a systematic way, the similarities, and yet, the differences between these two types of stability, and we highlight the symmetry that exists between them. We also illustrate how results on the stability of continuous-time systems are conveyed to the stability of discrete-time systems through the proposed techniques. It should be mentioned that the results on Schur–Cohn stability are known to be harder to obtain than Routh–Hurwitz stability ones, giving more credibility to the proposed approach. |
| first_indexed | 2024-03-09T12:24:06Z |
| format | Article |
| id | doaj.art-c5765f9d8f56446f94bf0b3c66ee8330 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T12:24:06Z |
| publishDate | 2022-03-01 |
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| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-c5765f9d8f56446f94bf0b3c66ee83302023-11-30T22:36:55ZengMDPI AGSymmetry2073-89942022-03-0114360310.3390/sym14030603Symmetric Properties of Routh–Hurwitz and Schur–Cohn Stability CriteriaZiad Zahreddine0Mathematics Division, College of Engineering, Kuwait College of Science and Technology, Al Jahraa 13133, KuwaitIt is often noticed in the literature that some key results on the stability of discrete-time systems of difference equations are obtained from their corresponding results on the stability of continuous-time systems of differential equations using suitable conformal mappings or bilinear transformations. Such observations lead to the search for a unified approach to the study of root distribution for real and complex polynomials, with respect to the left-half plane for continuous-time systems (Routh–Hurwitz stability) and with respect to the unit disc for discrete-time systems (Schur–Cohn stability). This paper is a further contribution toward this objective. We present, in a systematic way, the similarities, and yet, the differences between these two types of stability, and we highlight the symmetry that exists between them. We also illustrate how results on the stability of continuous-time systems are conveyed to the stability of discrete-time systems through the proposed techniques. It should be mentioned that the results on Schur–Cohn stability are known to be harder to obtain than Routh–Hurwitz stability ones, giving more credibility to the proposed approach.https://www.mdpi.com/2073-8994/14/3/603Routh–Hurwitz stabilitySchur–Cohn stabilitycontinuous-time systems of differential equationsdiscrete-time systems of difference equations |
| spellingShingle | Ziad Zahreddine Symmetric Properties of Routh–Hurwitz and Schur–Cohn Stability Criteria Symmetry Routh–Hurwitz stability Schur–Cohn stability continuous-time systems of differential equations discrete-time systems of difference equations |
| title | Symmetric Properties of Routh–Hurwitz and Schur–Cohn Stability Criteria |
| title_full | Symmetric Properties of Routh–Hurwitz and Schur–Cohn Stability Criteria |
| title_fullStr | Symmetric Properties of Routh–Hurwitz and Schur–Cohn Stability Criteria |
| title_full_unstemmed | Symmetric Properties of Routh–Hurwitz and Schur–Cohn Stability Criteria |
| title_short | Symmetric Properties of Routh–Hurwitz and Schur–Cohn Stability Criteria |
| title_sort | symmetric properties of routh hurwitz and schur cohn stability criteria |
| topic | Routh–Hurwitz stability Schur–Cohn stability continuous-time systems of differential equations discrete-time systems of difference equations |
| url | https://www.mdpi.com/2073-8994/14/3/603 |
| work_keys_str_mv | AT ziadzahreddine symmetricpropertiesofrouthhurwitzandschurcohnstabilitycriteria |