In this work we develop necessary and sufficient conditions for describing the family of anti-Hurwitz polynomials, introduced by Vergara-Hermosilla et al. in [1]. Specifically, we studied a dual version of the Theorem of Routh-Hurwitz and present explicit criteria for polynomials of low order and derivatives. Another contribution of this work is establishing a dual version of the Hermite-Biehler Theorem. To this aim, we give extensions of the boundary crossing Theorems and a zero exclusion principle for anti-Hurwitz polynomials.
References
[1]
Vergara-Hermosilla, G., Matignon, D. and Tucsnak, M. (2020) Asymptotic Behaviour of a System Modelling Rigid Structures Floating in a Viscous Fluid. hal-02475583, Version 1.
[2]
Gantmacher, F.R. (1959) Matrix Theory. Chelsea publishing, New York.
[3]
Gantmacher, F.R. (1959) The Theory of Matrices. Chelsea publishing, New York.
[4]
Gantmacher, F.R. (2012) Elementary stability and bifurcation theory, Springer Science & Business Media, New York.
[5]
Chappellat, H., Mansour, M. and Bhattacharyya, S.P. (1990) Elementary Proofs of Some Classical Stability Criteria. IEEE Transactions on Education, 33, 232-239.
https://doi.org/10.1109/13.57067
[6]
Holtz, O. (2003) Hermite-Biehler, Routh-Hurwitz, and Total Positivity. Linear Algebra and Its Applications, 372, 105-110.
https://doi.org/10.1016/S0024-3795(03)00501-9
[7]
Fettweis, A. (2016) A New Approach to Hurwitz Polynomials in Several Variables. Circuits, Systems and Signal Processing, 5, 405-417.
https://doi.org/10.1007/BF01599617
[8]
Vergara-Hermosilla, G. (2020) Relations between Fractional Calculus and Interactions Fluid-Structure. hal-02506981, Version 1.
[9]
Vergara-Hermosilla, G. and Matignon, D. and Tucsnak, M. (2020) Asymptotic Behaviour of a System Modelling Rigid Structures Floating in a Viscous Fluid. hal-02475576v2, Version 2.
