The paper presents new rnethodology liow to decompose the higlh dimensional LTI (linear time invariant) systam with both distinct and repeated eigenvalues of the transition matrix into a set of first-order LTI models, which could be combined to achieve approximation of the original dynamics. As a tool, the Sylvester’s theorems are used to design the filter bank and parameters of the firstorder models (transition values). At the end, the practical examples are shown and the next steps of research of the decomposition theory are indicated.