Dynamic observer-based control for fractional-order uncertain linear systems

ABSTRACT

This paper addresses the problem of dynamic observer-based control for fractional-order linear uncertain systems. By constructing a new linearising change of variables, the conditions for designing the observer and controller gains are obtained in terms of solutions to a set of linear matrix inequalities (LMIs) even in the presence of uncertainties in system, input and output matrices simultaneously. Meanwhile, owing to having additional degrees of freedom in the designed observer structure, the proposed methods have no equality constraint, which is needed by using Luenberger-type observer. Numerical examples are given to illustrate the benefits and the effectiveness of the proposed method.

Keywords:

• Fractional-order systems
• dynamic observer
• linear matrix inequalities

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the Funds of the National Natural Science Foundation of China (Grant Nos. 61621004 and 61420106016), and the Research Fund of State Key Laboratory of Synthetical Automation for Process Industries (Grant No. 2018ZCX03).

Notes on contributors

He Li

He Li received the B.S. degree in Mechanical design manufacturing and automation from Shenyang Ligong University, Liaoning, China, in 2010, the M.S. degree in Mathematics and Applied Mathematics from Shenyang Normal University, Liaoning, China, in 2014. He is currently pursuing the Ph.D. degree at the College of Information Science and Engineering, Northeastern University. His current research interests include robust and fault-tolerant control, fault detection, fractional-order systems.

Guang-Hong Yang

Guang-Hong Yang (SM'04) received the B.S. and M.S. degrees in Mathematics, and Ph.D. degree in control theory and control engineering with Northeast University, Shenyang, China, in 1983, 1986, and 1994, respectively. From 2001 to 2005, he was a Research Scientist/Senior Research Scientist with the National University of Singapore, Singapore. He is currently a Professor and the dean with the College of Information Science and Engineering, Northeastern University. His current research interests include fault-tolerant control, fault detection and isolation, cyber–physical systems, and robust control. He is a Deputy Editor-in-Chief for the Journal of Control and Decision, an Editor for the International Journal of Control, Automation and Systems, and an Associate Editor for the International Journal of Systems Science, the IET Control Theory and Applications and the IEEE Transactions on Fuzzy Systems.