Section: New Results

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

In [7], we present new computer algebra based methods for testing the structural stability of n-D discrete linear systems (with $n\ge 2$). More precisely, they 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.