## 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
${\u2102}^{n}$ ) 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.