Handelman's Positivstellensatz for polynomial matrices positive definite   on polyhedra
  In this paper we give a matrix version of Handelman's Positivstellensatz [1], representing polynomial matrices which are positive definite on convex, compact polyhedra. Moreover, we propose also a procedure to find such a representation. As a corollary of Handelman's theorem, we give a special case of Schm\"udgen's Positivstellensatz for polynomial matrices positive definite on convex, compact polyhedra. 
C\^ong-Tr\`inh L\^e and Thi-Hoa-Binh Du
math.AG