Journal of Systems Engineering and Electronics ›› 2021, Vol. 32 ›› Issue (3): 681-689.doi: 10.23919/JSEE.2021.000058

• CONTROL THEORY AND APPLICATION • Previous Articles     Next Articles

Stabilizing controller design for nonlinear fractional order systems with time varying delays

Abdollah AZIZI*(), Mehdi FOROUZANFAR()   

  1. 1 Department of Electrical Engineering, Ahvaz Branch, Islamic Azad University, Ahwaz 61349-37333, Iran
  • Received:2019-10-08 Online:2021-06-18 Published:2021-07-26
  • Contact: Abdollah AZIZI;
  • About author:|AZIZI Abdollah was born in 1983. He received his B.S. degree in power transmission networks from Boroujerd Islamic Azad University in 2012 and M.S. degree in control engineering from Boroujerd Islamic Azad University in 2015. He is a Ph.D. candidate student in control engineering at Department of Electrical Engineering, Ahvaz Branch, Islamic Azad University. His research focuses on fractional order controllers and systems, robust adaptive controllers and stability of nonlinear delayed systems. E-mail:||FOROUZANFAR Mehdi was born in 1983. He received his M.S. and Ph.D. degrees in control-electrical engineering from Amirkabir Industrial University, Tehran, Iran, in 2009, and from Sahand Industrial University, Tabriz, Iran, in 2017, respectively. Since 2017, He has been a faculty member of Department of Electrical Engineering, Islamic Azad University, Iran. His main areas of research interest are active fault detection & fault tolerance control, nonlinear system, identification, artificial intelligence, and cyber physical system. E-mail:


To deal with stabilizing of nonlinear affine fractional order systems subject to time varying delays, two methods for finding an appropriate pseudo state feedback controller are discussed. In the first method, using the Mittag-Lefler function, Laplace transform and Gronwall inequality, a linear stabilizing controller is derived, which uses the fractional order of the delayed system and the upper bound of system nonlinear functions. In the second method, at first a sufficient stability condition for the delayed system is given in the form of a simple linear matrix inequality (LMI) which can easily be solved. Then, on the basis of this result, a stabilizing pseudo-state feedback controller is designed in which the controller gain matrix is easily computed by solving an LMI in terms of delay bounds. Simulation results show the effectiveness of the proposed methods.

Key words: fractional order nonlinear system, time varying delay, state feedback control, linear matrix inequality (LMI), stabilizing