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On the distance to the instability border of hurwitz polynomials with coefficients that depend affinely onm parameters and a particular convexity property ofH n

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Abstract

Let

$$a(y,s) = \sum\limits_{i = 0}^{n - 1} {a_i s^i + s^n ,} $$

where the coefficientsa i=a i (y 1, ...,y m) depend affinely onm parameters. IfP is the zone of Hurwitz parameters, a formula is obtained to compute the distance of a pointy′ εP to the boundary ∂P. Furthermore, in the particular casem=1 it is proved that, if a line through the origin intersects the Hurwitz zone, the intersection will be either a finite interval or a half line. Necessary and sufficient conditions are given for the occurrence of each of these alternatives.

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Authors and Affiliations

  1. Departamento de Matematica, Universidad Nacional del Sur., Av. Alem No. 1253, 8000, Bahia Blanca, Argentina

    C. Robledo

  2. Comision de Investigaciones Cientificas de la Provincia de Buenos Aires (CIC), and Departamento de Ingenieria Electrica, Universidad Nacional del Sur., Av. Alem No. 1253, 8000, Bahia Blanca, Argentina

    A. Desages

  3. Comision Nacional de Investigaciones Cientificas y Tecnicas (CONICET), and Departamento de Matematica, Universidad Nacional del Sur., Av. Alem No. 1253, 8000, Bahia Blanca, Argentina

    H. Cendra

Authors
  1. C. Robledo
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  2. A. Desages
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  3. H. Cendra
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Robledo, C., Desages, A. & Cendra, H. On the distance to the instability border of hurwitz polynomials with coefficients that depend affinely onm parameters and a particular convexity property ofH n . Multidim Syst Sign Process 3, 45–61 (1992). https://doi.org/10.1007/BF01941017

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  • DOI: https://doi.org/10.1007/BF01941017

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