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.

Full Text

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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