Kybernetika 42 no. 5, 605-616, 2006

SPR0 substitutions and families of algebraic Riccati equations

G. Fernández-Anaya, J. C. Martínez García, Vladimír Kučera and D. Aguilar George


We study in this paper Algebraic Riccati Equations associated with single-input single-output linear time-invariant systems bounded in $H_{\infty }$-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 $H_{\infty}$-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 $H_{\infty }$-norm constraint and an upper bound on their corresponding McMillan degree.