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

Yacine Mohamed Bouzidi (1) , Alban Quadrat (2, 3) , Fabrice Rouillier (2, 4, 3)

1 GAIA - Géométrie, Algèbre, Informatique, Applications
2 OURAGAN - OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs
3 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
4 SU FM - Sorbonne Université - Faculté de Médecine

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.

Mots clés: Multidimensional systems; Computer algebra; Structural stability; Stability analysis

Domaines: Calcul formel [cs.SC]; Optimisation et contrôle [math.OC]; Automatique / Robotique

Yacine Mohamed Bouzidi, Alban Quadrat, Fabrice Rouillier. Certified Non-conservative Tests for the Structural Stability of Discrete Multidimensional Systems. Multidimensional Systems and Signal Processing, 2019, 30 (3), pp.31. ⟨10.1007/s11045-018-0596-y⟩. ⟨hal-01951765⟩