The presented paper summarizes the approaches to dynamic description of an induction machine and presents them from the view point of the modern theory of dynamic systems. Great impact has the selection of the particular state variables. It decides about the mutual dependency of calculated values. Despite of the fact that it is still a correct description of the same system, it influences the design of control structures. Only the matrix form underlines clearly the particular differences and shows what combinations of state variables are eligible to be employed in hierarchical control structures.