The effect of coordinate transformations on a class of control-system models

This study examines the effect of a transformation of variables upon the efficiency of a mathematical model in describing a real physical plant for purposes of optimal control, performance prediction, or both. The performance is defined by a generalized quadratic criterion of the minimum energy, minimal endpoint error type, and the plant to be controlled is assumed to be linear time-varying (at least in the small). The model is taken to be linear, but constant coefficient. It is shown that a "suitable" model may not exist if the plant is represented in the linear vector space most natural to physical reality, whereas such a model may exist if the plant behavior is mapped onto another linear vector space.