Robust Schur stability with polynomial parameters

We propose a stability test for discrete-time systems whose coefficients depend polynomially on some bounded parameters. The test is a particular form of Positivstellensatz, appeals to sum-of-squares polynomials and can be implemented as a semidefinite programming problem. Although implementable only in relaxed form, due to the necessity of limiting the degrees of the polynomial variables involved, the experiments show a good accuracy with degrees smaller than for other tests.