We introduce a “workable” notion of degree for non-homogeneous polynomial ideals and formulate prove ideal theoretic Bézout inequalities the sum two in terms this generators.

For a homogeneous polynomial with a non-zero discriminant, we interpret direct sum decomposability of the polynomial in terms of factorization properties of the Macaulay inverse system of its Milnor algebra. This leads to an if-and-only-if criterion for direct sum decomposability of such a polynomial, and to an algorithm for computing direct sum decompositions over any field, either of characte...

The problem addressed in this paper is the construction of homogeneous polynomial Lyapunov functions for linear systems with time-varying structured uncertainties. A sufficient condition for the existence of a homogeneous polynomial Lyapunov function of given degree is formulated in terms of a Linear Matrix Inequalities (LMI) feasibility problem. This condition turns out to be also necessary in...