摘要：The problem of deriving necessary and sufficient conditions for positive definiteness of a Homogeneous Matrix Polynomial (HMP) defined on the unit simplex is considered. The obtained results clearly indicate the superiority of the proposed here solution approach over a classical theorem, which can be viewed as a particular case of them. The main results are applicable for the solution of the stability analysis problem for a class of uncertain linear systems. It is shown that the proved exact conditions generalize and improve (in sense of conservatism reduction) two recent results, aimed at solving the same problem. The presented approach is illustrated by a comparative numerical example.
