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Absolute Stability of Nonlinear Systems with Piecewise Linear Sector Condition

by Amin Rezaei, Farzad Hashemzade
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 134 - Number 9
Year of Publication: 2016
Authors: Amin Rezaei, Farzad Hashemzade
10.5120/ijca2016908000

Amin Rezaei, Farzad Hashemzade . Absolute Stability of Nonlinear Systems with Piecewise Linear Sector Condition. International Journal of Computer Applications. 134, 9 ( January 2016), 15-18. DOI=10.5120/ijca2016908000

@article{ 10.5120/ijca2016908000,
author = { Amin Rezaei, Farzad Hashemzade },
title = { Absolute Stability of Nonlinear Systems with Piecewise Linear Sector Condition },
journal = { International Journal of Computer Applications },
issue_date = { January 2016 },
volume = { 134 },
number = { 9 },
month = { January },
year = { 2016 },
issn = { 0975-8887 },
pages = { 15-18 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume134/number9/23942-2016908000/ },
doi = { 10.5120/ijca2016908000 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T23:33:44.391292+05:30
%A Amin Rezaei
%A Farzad Hashemzade
%T Absolute Stability of Nonlinear Systems with Piecewise Linear Sector Condition
%J International Journal of Computer Applications
%@ 0975-8887
%V 134
%N 9
%P 15-18
%D 2016
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The circle theorem is one of the most important methods for study of absolute stability of nonlinear systems. In circle theorem, it is assumed that the nonlinearity term is located between linear bounds of a typical sector. In this paper the absolute stability of nonlinear systems with generalized sector condition is studied in which the bounds of the sector are piecewise linear in general. Therefore this method could be applied to the sector with nonlinear bounds. In this paper using modified Nyquist criterion, it is proved that the study of absolute stability of a nonlinear system using circle theorem could be reduced to the study of stability of equalized linear system. The aim of this paper is to define a pseudo circle region that the Nyquist plot of the linear system with nonlinearity in sector condition with piecewise bounds doesn’t have any intersection with that region and encircle it

References
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  3. H. Khalil, Nonlinear Systems. Upper Saddle River, NJ: Prentice-Hall, 1996.
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  6. A. Megretski and A. Rantzer, “system analysis via integral quadratic constraints,” IEEE Trans. Automat. Contr., vol. 42, pp. 819–830, May 1997.
  7. Amin Rezaei, Linear Control Systems, 6th, Pouran Pazhuhesh Pub., Tehran, Iran, 2015.
Index Terms

Computer Science
Information Sciences

Keywords

Circle theorem Lemma Non linear systems

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