D. Z. Arov Division of Applied Mathematics and Informatics, Institute of Physics and Mathematics, South-Ukrainian Pedagogical University, Odessa, 65020, Ukraine
M. A. Kaashoek Department of Mathematics, Vrije Universiteit, Amsterdam, The Netherlands
D. R. Pik Faculty of Social and Behavioural Sciences, University of Amsterdam, Amsterdam, The Netherlands
The Riccati inequality and equality are studied for infinite dimensional linear discrete time stationary systems with respect to the scattering supply rate. The
results obtained are an addition to and based on our earlier work on the Kalman-Yakubovich-Popov inequality in [6]. The main theorems are closely related to the
results of Yu. M. Arlinskiĭ in [3]. The main difference is that we do not assume the original system to be a passive scattering system, and we allow the solutions of the Riccati inequality and equality to satisfy weaker conditions.
D. Z. Arov Division of Applied Mathematics and Informatics, Institute of Physics and Mathematics, South-Ukrainian Pedagogical University, Odessa, 65020, Ukraine
M. A. Kaashoek Department of Mathematics, Vrije Universiteit, Amsterdam, The Netherlands
D. R. Pik Faculty of Social and Behavioural Sciences, University of Amsterdam, Amsterdam, The Netherlands
D. Z. Arov, M. A. Kaashoek, and D. R. Pik, Generalized solutions of Riccati equalities and inequalities, Methods Funct. Anal. Topology 22
(2016), no. 2, 95-116.
BibTex
@article {MFAT840,
AUTHOR = {Arov, D. Z. and Kaashoek, M. A. and Pik, D. R.},
TITLE = {Generalized solutions of Riccati equalities and inequalities},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {22},
YEAR = {2016},
NUMBER = {2},
PAGES = {95-116},
ISSN = {1029-3531},
MRNUMBER = {MR3522854},
ZBLNUMBER = {06665382},
URL = {http://mfat.imath.kiev.ua/article/?id=840},
}
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