joint work with

In this presentation, we discuss the theory of dissipa-tiveness of systems described by linear constant coefcient PDE's with respect to supply rates that are quadratic dif-ferential forms in the variables and their derivatives. The main issue considered is the equivalence of global and local dissipativeness. This leads to the construction of the storage function, the ux, and the dissipation rate. We show that mathematically this leads to Hilbert's 17-th problem on the factorization of a polynomial in n variables as a sum of squares. 1