Time-domain and parametric L 2 -properties corresponding to Popov inequality

Mihail Voicu; Octavian Pastravanu

Kybernetika (2002)

  • Volume: 38, Issue: 5, page [617]-629
  • ISSN: 0023-5954

Abstract

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For Popov’s frequency-domain inequality a general solution is constructed in L 2 , which relies on the strict positive realness of a generating function. This solution allows revealing time-domain properties, equivalent to the fulfilment of Popov’s inequality in the frequency-domain. Particular aspects occurring in the dynamics of the linear subsystem involved in Popov’s inequality are further explored for step response, as representing a usual characterization in control system analysis. It is also shown that such behavioural particularities are directly related to the BIBO stability of the linear subsystem.

How to cite

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Voicu, Mihail, and Pastravanu, Octavian. "Time-domain and parametric $L^2$-properties corresponding to Popov inequality." Kybernetika 38.5 (2002): [617]-629. <http://eudml.org/doc/33608>.

@article{Voicu2002,
abstract = {For Popov’s frequency-domain inequality a general solution is constructed in $L^2$, which relies on the strict positive realness of a generating function. This solution allows revealing time-domain properties, equivalent to the fulfilment of Popov’s inequality in the frequency-domain. Particular aspects occurring in the dynamics of the linear subsystem involved in Popov’s inequality are further explored for step response, as representing a usual characterization in control system analysis. It is also shown that such behavioural particularities are directly related to the BIBO stability of the linear subsystem.},
author = {Voicu, Mihail, Pastravanu, Octavian},
journal = {Kybernetika},
keywords = {Popov’s inequality; BIBO stability; Popov's inequality; BIBO stability},
language = {eng},
number = {5},
pages = {[617]-629},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Time-domain and parametric $L^2$-properties corresponding to Popov inequality},
url = {http://eudml.org/doc/33608},
volume = {38},
year = {2002},
}

TY - JOUR
AU - Voicu, Mihail
AU - Pastravanu, Octavian
TI - Time-domain and parametric $L^2$-properties corresponding to Popov inequality
JO - Kybernetika
PY - 2002
PB - Institute of Information Theory and Automation AS CR
VL - 38
IS - 5
SP - [617]
EP - 629
AB - For Popov’s frequency-domain inequality a general solution is constructed in $L^2$, which relies on the strict positive realness of a generating function. This solution allows revealing time-domain properties, equivalent to the fulfilment of Popov’s inequality in the frequency-domain. Particular aspects occurring in the dynamics of the linear subsystem involved in Popov’s inequality are further explored for step response, as representing a usual characterization in control system analysis. It is also shown that such behavioural particularities are directly related to the BIBO stability of the linear subsystem.
LA - eng
KW - Popov’s inequality; BIBO stability; Popov's inequality; BIBO stability
UR - http://eudml.org/doc/33608
ER -

References

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  1. Doetsch G., Funktional Transformationen, In: Mathematische Hilfsmittel des Inginieurs, Vol. I (R. Sauer, I. Szabo, eds.), Springer, Berlin 1967, pp. 232–484 (1967) MR0221799
  2. Föllinger O., Nichtlineare Regelungen, Oldenbourg, München 1993 Zbl0487.93002
  3. Roïtenberg I. N., Théorie du contrôle automatique, Publishing House Mir, Moscow 1974 Zbl0302.93001
  4. Wen J. T., 10.1109/9.7263, IEEE Trans. Automat. Control 33 (1988), 988–992 (1988) Zbl0664.93013MR0959031DOI10.1109/9.7263

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