Robust stability of non linear time varying systems

Ezra Zeheb

Kybernetika (1999)

  • Volume: 35, Issue: 4, page [415]-428
  • ISSN: 0023-5954

Abstract

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Systems with time-varying non-linearity confined to a given sector (Luré type) and a linear part with uncertainty formulated by an interval transfer function, are considered. Sufficient conditions satisfying the Popov criterion for stability, which are computationally tractable, are derived. The problem of checking the Popov criterion for an infinite set of systems, is reduced to that of checking the Popov criterion for a finite number of fixed coefficient systems, each in a prescribed frequency interval. Illustrative numerical examples are provided.

How to cite

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Zeheb, Ezra. "Robust stability of non linear time varying systems." Kybernetika 35.4 (1999): [415]-428. <http://eudml.org/doc/33437>.

@article{Zeheb1999,
abstract = {Systems with time-varying non-linearity confined to a given sector (Luré type) and a linear part with uncertainty formulated by an interval transfer function, are considered. Sufficient conditions satisfying the Popov criterion for stability, which are computationally tractable, are derived. The problem of checking the Popov criterion for an infinite set of systems, is reduced to that of checking the Popov criterion for a finite number of fixed coefficient systems, each in a prescribed frequency interval. Illustrative numerical examples are provided.},
author = {Zeheb, Ezra},
journal = {Kybernetika},
keywords = {Popov criterion; stability; time-varying nonlinearity; Lur’e type nonlinearity; interval transfer function; Popov criterion; stability; time-varying nonlinearity; Lur'e type nonlinearity; interval transfer function},
language = {eng},
number = {4},
pages = {[415]-428},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Robust stability of non linear time varying systems},
url = {http://eudml.org/doc/33437},
volume = {35},
year = {1999},
}

TY - JOUR
AU - Zeheb, Ezra
TI - Robust stability of non linear time varying systems
JO - Kybernetika
PY - 1999
PB - Institute of Information Theory and Automation AS CR
VL - 35
IS - 4
SP - [415]
EP - 428
AB - Systems with time-varying non-linearity confined to a given sector (Luré type) and a linear part with uncertainty formulated by an interval transfer function, are considered. Sufficient conditions satisfying the Popov criterion for stability, which are computationally tractable, are derived. The problem of checking the Popov criterion for an infinite set of systems, is reduced to that of checking the Popov criterion for a finite number of fixed coefficient systems, each in a prescribed frequency interval. Illustrative numerical examples are provided.
LA - eng
KW - Popov criterion; stability; time-varying nonlinearity; Lur’e type nonlinearity; interval transfer function; Popov criterion; stability; time-varying nonlinearity; Lur'e type nonlinearity; interval transfer function
UR - http://eudml.org/doc/33437
ER -

References

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  4. Fruchter G., Srebro U., Zeheb E., 10.1093/imamci/14.4.333, IMA J. Math. Control Inform. 14 (1997), 333–351 (1997) Zbl0896.93027MR1492837DOI10.1093/imamci/14.4.333
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  8. Popov V. M., Absolute stability of nonlinear systems of automatic control, Translated from Automatika i Telemekhanika 22 (1961), 961–979 (1961) Zbl0107.29601MR0133563
  9. Rozenvasser E. N., The absolute stability of non–linear systems, Translated from Automatika i Telemekhanika 24 (1963), 304–313 (1963) MR0160996
  10. Siljak D., 10.1016/0005-1098(69)90079-X, Automatica 5 (1969), 385–387 (1969) Zbl0179.41203DOI10.1016/0005-1098(69)90079-X
  11. Siljak D., Polytopes of nonnegative polynomials, In: Proc. of the American Control Conf. (ACC), Pittsburgh 1989, pp. 193-199 (1989) 
  12. Zeheb E., Robust stability of non–linear time varying systems, In: Proc. of the 5th IEEE Mediterranean Conf. on Control and Systems, Paphos 1997 

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