Obstructions to Genericity in Study of Parametric Problems in Control Theory

Motivation: Problems from control theory often involve a set of physical parameters , for instance, masses, spring constants, and damping coefficients with mechanical systems, or resistances, capacitances, and inductances with electrical circuits. The structural properties of the control system may depend crucially on the specific choice of concrete parameter values. In many relevant examples, a system is generically controllable (i.e., controllable for almost all possible parameter values), but becomes uncontrollable when certain relations between the parameters are fulfilled. It has been shown for many system classes of practical interest that controlla-bility amounts to the torsion–freeness of a module associated to the system.