Conservative dilations of dissipative N-D systems: the commutative and non-commutative settings

We establish the existence of conservative dilations for various types of dissipative non-commutative N-D systems. As a corollary, the criteria for existence of conservative dilations of corresponding dissipative commutative N-D systems are obtained. We show that such a criterion is fulfilled for all dissipative commutative Givone-Roesser systems, however there are also types of commutative N-D systems for which this criterion is fulfilled not for all dissipative systems. New results announced in this short paper appear without proofs, which we intend to present elsewhere.