On Stability of Parametrized Families of Polynomials and Matrices
The Schur and Hurwitz stability problems for a parametric polynomial family as well as the Schur stability problem for a compact set of real matrix family are considered. It is established that the Schur stability of a family of real matrices 𝒜 is equivalent to the nonsingularity of the family {𝐴2−2...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/687951 |
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| _version_ | 1832557129287860224 |
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| author | Handan Akyar Taner Büyükköroğlu Vakıf Dzhafarov |
| author_facet | Handan Akyar Taner Büyükköroğlu Vakıf Dzhafarov |
| author_sort | Handan Akyar |
| collection | DOAJ |
| description | The Schur and Hurwitz stability problems for a parametric polynomial
family as well as the Schur stability problem for a compact set of real
matrix family are considered. It is established that the Schur stability
of a family of real matrices 𝒜 is equivalent to the nonsingularity
of the family {𝐴2−2𝑡𝐴+𝐼∶𝐴∈𝒜,𝑡∈[−1,1]} if 𝒜 has at
least one stable member. Based on the Bernstein expansion of a
multivariable polynomial and extremal properties of a multilinear
function, fast algorithms are suggested. |
| format | Article |
| id | doaj-art-ccbb82914b244791862c7c60fafb161d |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ccbb82914b244791862c7c60fafb161d2025-02-03T05:43:41ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/687951687951On Stability of Parametrized Families of Polynomials and MatricesHandan Akyar0Taner Büyükköroğlu1Vakıf Dzhafarov2Department of Mathematics, Faculty of Science, Anadolu University, 26470 Eskisehir, TurkeyDepartment of Mathematics, Faculty of Science, Anadolu University, 26470 Eskisehir, TurkeyDepartment of Mathematics, Faculty of Science, Anadolu University, 26470 Eskisehir, TurkeyThe Schur and Hurwitz stability problems for a parametric polynomial family as well as the Schur stability problem for a compact set of real matrix family are considered. It is established that the Schur stability of a family of real matrices 𝒜 is equivalent to the nonsingularity of the family {𝐴2−2𝑡𝐴+𝐼∶𝐴∈𝒜,𝑡∈[−1,1]} if 𝒜 has at least one stable member. Based on the Bernstein expansion of a multivariable polynomial and extremal properties of a multilinear function, fast algorithms are suggested.http://dx.doi.org/10.1155/2010/687951 |
| spellingShingle | Handan Akyar Taner Büyükköroğlu Vakıf Dzhafarov On Stability of Parametrized Families of Polynomials and Matrices Abstract and Applied Analysis |
| title | On Stability of Parametrized Families of Polynomials and Matrices |
| title_full | On Stability of Parametrized Families of Polynomials and Matrices |
| title_fullStr | On Stability of Parametrized Families of Polynomials and Matrices |
| title_full_unstemmed | On Stability of Parametrized Families of Polynomials and Matrices |
| title_short | On Stability of Parametrized Families of Polynomials and Matrices |
| title_sort | on stability of parametrized families of polynomials and matrices |
| url | http://dx.doi.org/10.1155/2010/687951 |
| work_keys_str_mv | AT handanakyar onstabilityofparametrizedfamiliesofpolynomialsandmatrices AT tanerbuyukkoroglu onstabilityofparametrizedfamiliesofpolynomialsandmatrices AT vakıfdzhafarov onstabilityofparametrizedfamiliesofpolynomialsandmatrices |