Observer-based finite-time control of linear fractional-order systems with interval time-varying delay

Abstract

In this paper, the problem of finite-time observer-based control for linear fractional-order systems with interval time-varying delay is studied. The delay is assumed to vary within an interval with known lower and upper bounds. A new proposition on estimating Caputo derivatives of quadratic functions is given. Based on the proposed result, delay-dependent sufficient conditions for finite-time stability and for designing state feedback controllers and observer gains for observer-based control problem are established in terms of a tractable linear matrix inequality and Mittag–Leffler function. A numerical example with simulation is given to demonstrate the effectiveness of the proposed method.

Keywords:

• Fractional calculus
• observer control
• finite-time stability
• feedback stabilisation
• time-variable delay
• linear matrix inequalities

Acknowledgments

This work was supported by the Chiang Mai University, Thailand and Vietnam Academy of Science and Technology. The authors would like to thank anonymous reviewers for their valuable comments and suggestions, which allow us to improve the presentation and quality of this paper.

Disclosure statement

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

Additional information

Funding

This work was supported by the Chiang Mai University, Thailand and Vietnam Academy of Science and Technology.

Notes on contributors

Nguyen T. Thanh

Nguyen T. Thanh received the B.Sc. and Ph.D. degrees in mathematics from Hanoi National University in 2004 and 2015, respectively. He is now a senior lecturer and associate professor at Department of Mathematics, Hanoi Mining and Geology University. His research interests include stability analysis, fractional calculus, control theory and applications.

Piyapong Niamsup

Piyapong Niamsup received the B.Sc. degree in mathematics from Chiang Mai University, Thailand in 1992. He also received the M.Sc. and Ph.D. degrees in mathematics from University of Illinois at Urbana-Champaign, USA in 1995 and 1997, respectively. In 1997, he joined the Department of Mathematics, Faculty of Science, Chiang Mai University, Thailand as a lecturer, where he became an associate professor in 2006. His research interests include complex dynamics, stability theory, switched systems, chaos synchronization, and discrete-time events.

Vu N. Phat

Vu N. Phat received the B.Sc. and Ph.D. degrees in mathematics at the former USSR Bacu State University, USSR in 1975 and 1984, respectively. He received the D. Sc. Degree in mathematics at the Institute of Mathematics, Polish Academy of Sciences, Poland in 1995. Currently, he works as a professor at the Institute of Mathematics, Vietnam Academy of Science and Technology, Vietnam. He is the author/co-author of two monographs and more than 100 refereed journal papers. His research interests include systems and control theory, optimization techniques, stability analysis, fractional calculus, and time-delay systems.