We study in this paper Algebraic Riccati Equations associated with single-input single-output linear time-invariant systems bounded in H∞-norm. Our study is focused in the characterization of families of Algebraic Riccati Equations in terms of strictly positive real (of zero relative degree) substitutions applied to the associated H∞-norm bounded system, each substitution characterizing then a particular member of the family. We also consider here Algebraic Riccati Equations associated with systems characterized by both an H∞
-norm constraint and an upper bound on their corresponding McMillan degree.
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.