Open Access

# Generalized solutions of Riccati equalities and inequalities

### Abstract

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.

Key words: Discrete time-invariant systems, scattering supply rate, passive systems, Riccati equality, Riccati inequality, Kalman-Yakubovich-Popov inequality.

### Article Information

 Title Generalized solutions of Riccati equalities and inequalities Source Methods Funct. Anal. Topology, Vol. 22 (2016), no. 2, 95-116 MathSciNet MR3522854 zbMATH 06665382 Milestones Received 07/02/2016; Revised 03/03/2016 Copyright The Author(s) 2016 (CC BY-SA)

### Authors Information

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

### Citation Example

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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