$D$-models of dynamic systems and their application

A model is proposed for a dynamic system specified as an input-to-output mapping. The motion in the state space is described by a semi-group of shift operators. The model describes linear stationary systems with a finite dimensional state space. Conditions for the existence of a finite dimensional model realization. The procedure for design of multi-input multi-output system with the use of the method of $D$-models is given. The method is extended to the class of nonlinear models of the Urysson operator type.