On the dissipativity of pseudorational behaviors

This paper studies dissipativity for a class of infinite-dimensional systems, called pseudorational, in the behavioral context. A basic equivalence condition for dissipativity is established as a generalization of the finite-dimensional counterpart. For its proof, we derive a new necessary and sufficient condition for entire functions of exponential type (in the Paley-Wiener class) to be symmetrically factorizable. These results play crucial roles in characterizing dissipative behaviors and LQ-optimal behaviors in pseudorational settings.