Geodesic
SPR0 substitutions and families of algebraic Riccati equations
Kybernetika, Tome 42 (2006) no. 5, pp. 605-616

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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.
Classification : 15A24, 93B25, 93B36
Keywords: linear time invariant systems; positive real substitutions; properties preservation; algebraic Riccati equations; $H_{\infty }$-norm bounded systems 
@article{KYB_2006__42_5_a5,
     author = {Fern\'andez-Anaya, G. and Mart{\'\i}nez Garc{\'\i}a, J. C. and Ku\v{c}era, Vladim{\'\i}r and Aguilar George, D.},
     title = {SPR0 substitutions and families of algebraic {Riccati} equations},
     journal = {Kybernetika},
     pages = {605--616},
     publisher = {mathdoc},
     volume = {42},
     number = {5},
     year = {2006},
     mrnumber = {2283508},
     zbl = {1249.93042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2006__42_5_a5/}
}
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Fernández-Anaya, G.; Martínez García, J. C.; Kučera, Vladimír; Aguilar George, D. SPR0 substitutions and families of algebraic Riccati equations. Kybernetika, Tome 42 (2006) no. 5, pp. 605-616. http://geodesic.mathdoc.fr/item/KYB_2006__42_5_a5/