We propose a new perspective on the identification of linear dynamic system using structural similarity. The proposal consists in the meaningful exploration of each model, specifically behavior of the state variable. The decomposition of the behavior of a state variable in different modes of behavior of a system, each one has a different set of weights and shows different patterns of behavior. These weights are more significant than eigenvalue to develop a new technique for identifying linear system and invariants over time. We use two methods based on different areas of knowledge such as linear algebra and statistics. This paper is a conceptual proof that enriches the implementation and validity not only from point of view algorithmic likewise physic mathematical.