Section: New Results

Certified non-conservative tests for the structural stability of discrete multidimensional systems

In collaboration with Fabrice Rouillier (Inria Paris, Ouragan), in [18], we propose a new approach for testing the stability of $n$D systems. We first 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. Our results have been implemented in a Maple prototype.