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Generalized solutions of Riccati equalities and inequalities


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.

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TitleGeneralized solutions of Riccati equalities and inequalities
SourceMethods Funct. Anal. Topology, Vol. 22 (2016), no. 2, 95-116
MathSciNet   MR3522854
zbMATH 06665382
Milestones  Received 07/02/2016; Revised 03/03/2016
CopyrightThe 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

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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.


@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 = {},


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