Positivstellensatz for Trigonometric Polynomials and Multidimensional Stability Tests

We propose a Positivstellensatz for trigonometric polynomials that is simpler than its correspondent for polynomials of real variable. Using it, we give a stability test for multidimensional systems, consisting of checking the feasibility of a linear matrix inequality. The same result is used for a robust stability test for systems whose coefficients depend polynomially on some bounded parameters. The new tests are either more accurate or faster than previous ones