Dissipative Distributed

A controllable distributed dynamical system described by a system of linear constant-coeecient partial diierential equations is said to be conservative if for compact support trajectories the integral of the supply rate is zero. It is said to be dissipative if this integral is non-negative. The question that we consider is whether these global versions of conservation and dissipativeness are equivalent to local versions, involving a storage function and a dissipation rate. It is shown that this is indeed the case, provided we consider latent variable representations.