Certified Non-conservative Tests for the Structural Stability of Multidimensional Systems

Yacine Bouzidi 1 Alban Quadrat 1 Fabrice Rouillier 2, 3
1 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : In this paper, we present new computer algebra based methods for testing the structural stability of n-D discrete linear systems (with n >= 2). More precisely, we show that the standard characterization of the structural stability of a multivariate rational transfer function (namely, the denominator of the transfer function does not have solutions in the unit polydisc of \C^n) is equivalent to the fact that a certain system of polynomials does not have real solutions. We then use state-of-the-art computer algebra algorithms to check this last condition, and thus the structural stability of multidimensional systems.
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https://hal.inria.fr/hal-01571230
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Submitted on : Tuesday, August 1, 2017 - 6:02:11 PM
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Yacine Bouzidi, Alban Quadrat, Fabrice Rouillier. Certified Non-conservative Tests for the Structural Stability of Multidimensional Systems. [Research Report] RR-9085, INRIA Lille - Nord Europe; INRIA Paris. 2017, pp.31. ⟨hal-01571230⟩

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