Robust stability and stabilization of fractional-order systems with polytopic uncertainties via homogeneous polynomial parameter-dependent matrix forms

Abstract

This paper addresses the robust stability and stabilization problems for fractional-order systems with polytopic uncertainties. By introducing homogeneous polynomial parameter-dependent matrix forms, the robust stability and stabilization conditions can be expressed as square matricial representation (SMR) of matrix forms, which is finally reduced to solving linear matrix inequalities (LMIs). Since the auxiliary matrices are all homogeneous polynomial parameter-dependent, the proposed method is effective and less conservative than the existing results, which is illustrated by the final numerical examples.

Keywords:

• Fractional-order system
• polytopic uncertainty
• robust stability
• robust control

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [Grants [62073217, 61374030 and 61533012].

Notes on contributors

Siyou Luo

Siyou Luo received the BE degree in electronic engineering from the Fudan University, Shanghai, China, in 2020. He is currently pursuing the MA degree with the Department of Automation, Shanghai Jiao Tong University, Shanghai, China. His current research interests include fractional-order systems, robust control and 2D systems.

Jun-Guo Lu

Jun-Guo Lu received the BE and PhD degrees in control theory and control engineering from the Nanjing University of Science and Technology, Nanjing, China, in 1997 and 2002, respectively. From 2001 to 2003, he was a Postdoctoral Fellow with the Department of Automation, Shanghai Jiao Tong University, Shanghai, China. In 2003, he joined Shanghai Jiao Tong University, where he is currently a Professor with the Department of Automation. His current research interests include nonlinear output regulation theory and applications, fractional-order control systems, robot control and multirobot coordination, machine vision, and three-dimensional (3-D) digitalization.