A Mathematica procedure for the computation, parametrization and tuning of proper denominator assigning compensators for strictly proper plants

We consider linear, time invariant, multivariable systems which are assumed to be free of unstable hidden modes and whose input-output relation is described by a strictly proper transfer function matrix P(s) (the plant). In this paper we describe a Mathematica symbolic algebra procedure for the efficient computation and tuning of a proper compensator C(s) which, when employed in a unity feedback loop, will give rise to a closed loop system S(P, C) with a specific closed loop denominator D_C(s). The choice of a specific compensator is obtained via a graphics user interface which allows the user to shape the step responses of the closed loop system by fine tuning the real parameter that parametrize the family of compensators.