2022
DOI: 10.1155/2022/9404316
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On Robust Stability for Hurwitz Polynomials via Recurrence Relations and Linear Combinations of Orthogonal Polynomials

Abstract: In this contribution, we use the connection between stable polynomials and orthogonal polynomials on the real line to construct sequences of Hurwitz polynomials that are robustly stable in terms of several uncertain parameters. These sequences are constructed by using properties of orthogonal polynomials, such as the well-known three-term recurrence relation, as well as by considering linear combinations of two orthogonal polynomials with consecutive degree. Some examples are presented.

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Cited by 2 publications
(6 citation statements)
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“…Indeed, the location of the roots is directly related to the performance of the system. It is important to notice that some families of robustly stable polynomials (defined in terms of orthogonal polynomials) have been proposed in the literature [17][18][19], and the behavior of the roots in terms of the uncertain parameter has been studied [19].…”
Section: Definition 1 ([11]mentioning
confidence: 99%
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“…Indeed, the location of the roots is directly related to the performance of the system. It is important to notice that some families of robustly stable polynomials (defined in terms of orthogonal polynomials) have been proposed in the literature [17][18][19], and the behavior of the roots in terms of the uncertain parameter has been studied [19].…”
Section: Definition 1 ([11]mentioning
confidence: 99%
“…We point out that a similar procedure was used to construct robustly stable families of Hurwitz polynomials by using orthogonal polynomials on the real line [17,18], because there is a close connection between both theories [23,24]. General information about orthogonal polynomials on the real line can be found in [22,25].…”
Section: Robustly Stable Polynomials From Orthogonal Polynomialsmentioning
confidence: 99%
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