  It is well-understood that the robustness of mechanical and robotic control
systems depends critically on minimizing sensitivity to arbitrary
application-specific details whenever possible. For example, if a system is
defined and performs well in one particular Euclidean coordinate frame then it
should be expected to perform identically if that coordinate frame is
arbitrarily rotated or scaled. Similarly, the performance of the system should
not be affected if its key parameters are all consistently defined in metric
units or in imperial units. In this paper we show that a recently introduced
generalized matrix inverse permits performance consistency to be rigorously
guaranteed in control systems that require solutions to underdetermined and/or
overdetermined systems of equations.
