Semidefinite programming duality on n-D behaviors

A semidefinite programming (SDP) is recognized as a valuable numerical tool in the optimization theory. In this paper, we consider the SDP duality on n-dimensional (n-D) system described by high-order partial differential-algebraic equation in the behavioral framework. We derive an alternative condition for the nonnegativity and positivity of a 2n-variable polynomial matrix as a main result. This condition is applied to derive an alternative condition for checking dissipativity of an n-D behavior.