Pole assignment for continuous-time fractional order systems

Abstract

The problem of pole assignment for linear continuous-time commensurate fractional order systems is addressed. The closed-loop poles are assigned in the adequate stability region according to the fractional derivative order α in $\left[01\right]$ or in $\left[12\right]$. First, sufficient stability conditions are established for both cases. Then, link is made to a pole assignment procedure enabling one to ensure the closed-loop asymptotic stability. Furthermore, robustness of the pole assignment against parametric uncertainties for the fractional order differential system has been investigated for both cases. Finally, ease of application and effectiveness of the proposed approach are shown through a practical example.

Abbreviations: FOS: Fractional order system; LHP: left half plan; RHP: right half plan; LMI: linear matrix inequality

Keywords:

• Fractional order systems
• asymptotic stability
• pole assignment
• stability region
• parametric uncertainties

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Abdoualaziz Ben Braim

Abdoualaziz Ben Braim, has Master degree from Cadi Ayyad University in 2015, He is currently a Ph.D. student at Laboratory LAEPT of Faculty of Sciences-Semlalia Marrakech, Morocco. His interest is fractional-order systems, robustness and delay systems.

Fouad Mesquine

Fouad Mesquine, has Ph.D. and Doctorat of third cycle in 1997, 1992, respectively, both in automatic control from Cadi Ayyad University. He is currently a Professor at Faculty of Sciences-Semlalia at physics department, Marrakech, Morocco. His interest is constrained control systems, delay systems, fractional order systems, robustness and pole assignment techniques. He co-authored a book on saturated linear systems and is the co-author of several journal papers and conferences.