Classification of linear control systems with observation

We concern with the classification problem of time-invariant linear control systems (governed by ordinary differential equations) with observation. After giving the definition of linear, differentiable and topological equivalence in a unified way, we derive some properties on these three kinds of equivalence. The linear classification result is expressed explicitly in the two-dimensional case. In some sense, our linear classification result partially generalizes P. Brunovsky´s one on linear control systems without observation.