Topological equivalence canonical forms for linear multivariable systems without control

In this paper, we discuss the classification problem for linear time-invariant multivariable systems without control. It turns out that the observability and stability are invariant for topological equivalent systems. Abstract results concerning system decomposition according to eigenvalues and observability are obtained. Finally, as concrete examples, the topological equivalence canonical forms for a three dimensional system equipped with a scalar observation are presented explicitly.