An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials
An important problem related to the study of the robust stability of a linear system that presents variation in terms of an uncertain parameter consists of understanding the variation in the roots of a system’s characteristic polynomial in terms of the uncertain parameter. In this contribution, we p...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/20/4244 |
| _version_ | 1797573105756930048 |
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| author | Noé Martínez Luis E. Garza Gerardo Romero |
| author_facet | Noé Martínez Luis E. Garza Gerardo Romero |
| author_sort | Noé Martínez |
| collection | DOAJ |
| description | An important problem related to the study of the robust stability of a linear system that presents variation in terms of an uncertain parameter consists of understanding the variation in the roots of a system’s characteristic polynomial in terms of the uncertain parameter. In this contribution, we propose an algorithm to provide sufficient conditions on the uncertain parameter in such a way that a robustly stable family of polynomials has all of its zeros inside a specific subset of its stability region. Our method is based on the Rouché’s theorem and uses robustly stable polynomials constructed by using basic properties of orthogonal polynomials. |
| first_indexed | 2024-03-10T21:04:56Z |
| format | Article |
| id | doaj.art-a8cb227923864389a9d6dad1096755af |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T21:04:56Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a8cb227923864389a9d6dad1096755af2023-11-19T17:13:13ZengMDPI AGMathematics2227-73902023-10-011120424410.3390/math11204244An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable PolynomialsNoé Martínez0Luis E. Garza1Gerardo Romero2Unidad Académica Multidisciplinaria Reynosa Rodhe, Universidad Autónoma de Tamaulipas, Reynosa C.P. 88779, MexicoFacultad de Ciencias, Universidad de Colima, Colima C.P. 28040, MexicoUnidad Académica Multidisciplinaria Reynosa Rodhe, Universidad Autónoma de Tamaulipas, Reynosa C.P. 88779, MexicoAn important problem related to the study of the robust stability of a linear system that presents variation in terms of an uncertain parameter consists of understanding the variation in the roots of a system’s characteristic polynomial in terms of the uncertain parameter. In this contribution, we propose an algorithm to provide sufficient conditions on the uncertain parameter in such a way that a robustly stable family of polynomials has all of its zeros inside a specific subset of its stability region. Our method is based on the Rouché’s theorem and uses robustly stable polynomials constructed by using basic properties of orthogonal polynomials.https://www.mdpi.com/2227-7390/11/20/4244robust stabilitySchur polynomialsorthogonal polynomialsRouché’s theorem |
| spellingShingle | Noé Martínez Luis E. Garza Gerardo Romero An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials Mathematics robust stability Schur polynomials orthogonal polynomials Rouché’s theorem |
| title | An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials |
| title_full | An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials |
| title_fullStr | An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials |
| title_full_unstemmed | An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials |
| title_short | An Application of Rouché’s Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials |
| title_sort | application of rouche s theorem to delimit the zeros of a certain class of robustly stable polynomials |
| topic | robust stability Schur polynomials orthogonal polynomials Rouché’s theorem |
| url | https://www.mdpi.com/2227-7390/11/20/4244 |
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