Finite-time dissipative control design for one-sided Lipschitz nonlinear singular Caputo fractional order systems

ABSTRACT

This paper presents an efficient analytical approach for solving the problem of dissipative control in one-sided Lipschitz singular Caputo fractional-order systems subject to nonlinear perturbations. The approach is based on mathematical transformations, and fractional calculus. A state feedback controller is designed to ensure that the closed-loop system is regular, impulse-free, and finite-time bounded with a dissipativity performance index. The results are established using tractable strict linear matrix inequalities (LMIs) without any equality constraint. Two numerical examples are provided to demonstrate the effectiveness of the proposed approach.

KEYWORDS:

• Singular fractional-order systems
• one-sided Lipschitz condition
• uncertainty
• singularity value theory
• linear matrix inequalities

Acknowledgments

The authors sincerely thank the Editors and anonymous reviewers for their constructive comments that helped improve the quality and presentation of this paper.

Data availability statement

All data generated or analysed during this study are included in this article.

Disclosure statement

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

Additional information

Funding

The research of Mai Viet Thuan is funded by the Ministry of Education and Training of Vietnam under grant number B2023-TNA-15. The research of Nguyen Thi Phuong is funded by the Ministry of Education and Training of Vietnam under grant number B2022-MDA-02.

Notes on contributors

Nguyen Thi Phuong

Nguyen Thi Phuong received M.Sc. degree in Mathematics from Thai Nguyen University of Education, Thai Nguyen city, Viet Nam in 2010. Her research interests include stability analysis, control theory, singular systems and fractional-order systems.

Nguyen Huu Sau

Nguyen Huu Sau received the Ph.D.degree in Mathematics from the Institute of Mathematics, Hanoi, Vietnam, in 2018. His research interests include (Stability, State bounding) analysis, Singular systems, Time-delay systems, Fractional order systems, Positive systems.

Mai Viet Thuan

Mai Viet Thuan received M.Sc. and Ph.D. degrees in mathematics from the Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam, in 2009 and 2015, respectively. He began with Thai Nguyen University of Sciences, Thai Nguyen, Vietnam in 2007 where he is currently a lecturer in mathematics. His current research interests include systems and control theory, time-delay systems, neural networks, and fractional-order systems. Dr. Thuan is a reviewer of more than 20 international journals and he is the author or co-author of more than 45 journal papers.