Stabilisation of Takagi–Sugeno fuzzy singular fractional-order systems subject to actuator saturation

Abstract

In this paper, the stabilisation of fuzzy singular fractional-order systems (FOSs) with order $0<\nu <1$ is discussed. Firstly, the sufficient conditions of fuzzy singular FOSs with actuator saturation are proposed. Further, the stabilisation criteria are given when the fuzzy singular FOSs are reduced to singular FOSs, including those with equality constraints and without equality constraints. Then, based on the proposed stabilisation conditions, we can estimate the stability region by solving an optimisation problem. Finally, two numerical examples are given to verify the effectiveness of our results.

Keywords:

• Fractional-order systems
• singular systems
• fuzzy systems
• actuator saturation
• stabilisation
• linear matrix inequalities

Disclosure statement

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

Additional information

Notes on contributors

Xuefeng Zhang

Xuefeng Zhang received the B.Sc. degree in applied mathematics, the M.S. degree in control theory and control engineering, and the Ph.D. degree in control theory and control engineering from Northeastern University, Shenyang, China in 1989, 2004, and 2008, respectively, where he is currently with the School of Sciences. He has published more than 100 journal and conference papers and 3 books. He is the Associate Editor of IEEE Access and the Committee member of Technical Committee on Fractional and Control of Chinese Association of Automation. His research interests include fractional order control systems and singular systems.

Zhe Wang

Zhe Wang received the B.Sc.degree in mathematics and applied mathematics from Bohai University in 2018. She is currently pursuing the M.S. degree in operations research and cybernetics with Northeastern University, Shenyang, China, where she is also with the School of Sciences. Her research interests include fractional order systems, Takagi-Sugeno fuzzy systems and Switched systems.