On Positiveness of Matrix-Valued Polynomials and Robust Semidefinite Programming
Abstract
This report is devoted to the study of robust semidefinite programming. We show that to the issue of computing the worst-case optimal value of semidefinite programs depending polynomially upon a finite number of bounded scalar parameters, one may associate a countable family of standard semidefinite programs, whose optimal values converge monotonically towards the requested quantity. The results is linked to representation formula and positiveness criterion for matrix-valued polynomials.