On the state-space realizations of matrix fraction descriptions for multivariable systems

A new representative of the state is introduced. This makes a connection between the input/output description of the system (in terms of module theory) and the state-space description (in terms of abstract linear algebra) via the transfer function methods of Rosenbrock and the operator-form realization of Fuhrmann. The state and the realization are both expressed explicitly in terms of a minimal matrix fraction description of the transfer function matrix.