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

Topological equivalence canonical forms for linear multivariable systems without control