Algebraic manipulations of transfer function matrix via statespace approach will be given without referring to the symbolic manipulations involving the indeterminate s, for a linear continu-ous-time system (or, z, for a linear discrete-time system). The resultant transfer function is closely related to a state-space representation, and therefore is advantageous in realization, implementation, computer simulation and stability analysis. Furthermore, the design, implementation, and analysis of linear dynamic controllers, in the forms of 2-input-1-output and 2D (two degree of freedoms), are illustrated with numerical examples via the method proposed.

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