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Stability analysis of time-delayed linear fractional-order systems

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  • Control Theory
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Abstract

In this article, an exact and robust method for the determination of all the possible stability regions in the parametric space has been presented for the fractional order systems with time delay. Using the approach presented in this study, first, the transcendental terms have been eliminated from the characteristic equation and then, all the locations on the imaginary axis crossed by the roots and also their direction of crossing have been calculated. Finally, the concept of the stability as a function of the time delay has been described for a general class of linear fractional order systems with several commensurate delays. Prior to the conclusion, several examples have been given to validate the results of the proposed approach.

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Authors and Affiliations

  1. Department of Electrical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Mohammad Ali Pakzad

  2. Department of Electrical Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran

    Sara Pakzad

  3. Faculty of Electrical and Computer Engineering, K. N. Toosi University of Technology, Seyed-Khandan, P. O. Box 16315-1355, Tehran, Iran

    Mohammad Ali Nekoui

Authors
  1. Mohammad Ali Pakzad
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  2. Sara Pakzad
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  3. Mohammad Ali Nekoui
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Correspondence to Mohammad Ali Pakzad.

Additional information

Recommended by Editorial Board member Soohee Han under the direction of Editor Myotaeg Lim.

Mohammad Ali Pakzad was born in Tehran, Iran on September 1981. He received his B.S. degree in Electronics Engineering from Karaj Branch, Islamic Azad University, Iran in 2005, an M.Sc. degree in Control Engineering from Science and Research Branch, Islamic Azad University, Tehran, Iran in 2009. Currently he is a Ph.D. student in control engineering at Science and Research Branch, Islamic Azad University Tehran, Iran. His research interests include stability analysis of time-delayed systems, control systems theory, fractional order systems and model predictive control.

Sara Pakzad was born in Tehran, Iran on June 1984. She received her B.S. degree in Applied Mathematics from University of Kurdistan, Iran in 2007, an M.Sc. degree in Control Engineering from South Tehran Branch, Islamic Azad University, Iran in 2010. Her research interests include different aspects of mathematics in control, stability analysis of time-delayed systems, control systems theory, fractional order systems.

Mohammad Ali Nekoui was born in December 1952. He received his M.Sc. degree in Electrical Engineering from the University of Tehran in 1976, Diplome d’Espe cialisation in Instrume-ntation et Metrologie from Ecole Superieur d’ Electricite (SUPEL EC), France, in 1979 and his Ph.D. degree at the School of Electrical and Electronic Engineering in Computer and Control Department from University of Leeds, U.K. in 1997. Since 1980, he has been with the K.N.T. University of Technology. At present he is an Assistant Professor at the Faculty of Electrical and Computer Engineering of this university. His interest includes linear and nonlinear optimization, linear systems, optimal control, and different aspects of mathematics in control.

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Pakzad, M.A., Pakzad, S. & Nekoui, M.A. Stability analysis of time-delayed linear fractional-order systems. Int. J. Control Autom. Syst. 11, 519–525 (2013). https://doi.org/10.1007/s12555-012-0164-4

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  • DOI: https://doi.org/10.1007/s12555-012-0164-4

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