Degree bounds for polynomial verification of the matrix cube
- B. D. Chen and S. Lall.
- Proceedings of the IEEE Conference on Decision and Control, p. 4405--4410, 2006.
In this paper we consider the problem of how to computationally test whether a matrix inequality is positive semidefinite on a semialgebraic set. We propose a family of sufficient conditions using the theory of matrix Positivstellensatz refutations. When the semialgebraic set is a hypercube, we give bounds on the degree of the required certificate polynomials.