Integral sliding mode control for interconnected descriptor systems based on a reduced-order observer

Abstract

In this paper, a reduced-order observer-based integral sliding mode controller is designed for a class of interconnected descriptor systems. First, the observer matching condition is used to transform the interconnected descriptor system into an interconnected normal system. Based on the canonical form, a reduced-order observer is then designed to estimate the state variables of the interconnected descriptor system. In terms of the measurable output variables and the state variables of the proposed reduced-order observer, a sliding mode control scheme is developed to drive the state trajectories of the system to the sliding surface in a finite time and maintain a sliding motion thereafter. It is shown that at the existence of unknown matched disturbances, the proposed observer-based integral sliding mode control scheme can still ensure the asymptotic stability of the resultant closed-loop system. This is an obvious improvement of the existing observer-based sliding mode control methods in descriptor systems fields. Finally, an example is given to verify the effectiveness of the proposed method.

Keywords:

• Interconnected system
• integral sliding mode control
• reduced-order observer
• observer-based sliding mode controller
• descriptor system

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Jinghao Li http://orcid.org/0000-0002-9122-7184

Additional information

Funding

This work was supported by the Research Fund of State Key Laboratory of Synthetical Automation for Process Industries [grant number 2018ZCX23] and the Fundamental Research Funds for the Central Universities [grant numbers N180403020 and N182008004].

Notes on contributors

Rui Gao

Rui Gao received the B.S. degree in Mathematics from Northeastern University, China, in 2017. She is now pursuing the M.S. degree in Operational Research and Cybernetics, from Northeastern University, China. Her current research interests focus on sliding mode control, output feedback and descriptor systems.

Qingling Zhang

Qingling Zhang received B.S. and M.S. degrees from the Mathematics Department, and Ph.D. degree from the Automatic Control Department of Northeastern University, Shenyang, China, in 1982, 1986 and 1995, respectively. He finished his two-year Postdoctoral work from the Automatic Control Department of Northwestern Polytechnical University, Xian, China, in 1997. Since then he has been a Professor and serves the College of Science at Northeastern University as dean from 1997 to 2006. He was also a member of the University Teaching Advisory Committee of National Ministry of Education, and now he is vice chairman of the Chinese Biomathematics Association, member of technical committee on control theory of the Chinese Association of Automation, member of the Chinese Association of Mathematics and Chairman of Mathematics Association of Liaoning Province. He has published 16 books and more than 600 papers about control theory and applications. Prof. Zhang received 14 prizes from central and local governments for his research. He has also received the Gelden Scholarship from Australia in 2000. During these periods, he visited Hong Kong University, Seoul University, Alberta University, Lakehead University, Sydney University, Western Australia University, Windsor University, Hong Kong Polytechnic University and Kent University as a Research Associate, Research Fellow, Senior Research Fellow and Visiting Professor, respectively.

Jinghao Li

Jinghao Li received the B.S. degree in mathematics, the M.S. degree in systems theory and the Ph.D. degree in control theory and control engineering from Northeastern University, China, in 2011, 2013 and 2018, respectively. From September 2017 to March 2018, he was a Research Assistant with the Department of Applied Mathematics, The Hong Kong Polytechnic University. He is currently a Lecture with the College of Information Science and Engineering, Northeastern University. His current research interests include sliding mode control, descriptor systems, T-S fuzzy systems and cyber-physical systems.

Ding Zhai

Ding Zhai received the B.S. degree in automation, the M.S. degree in industry automation, and the Ph.D. degree in automation from Northeastern University, Shenyang, China, in 1992, 1999, and 2004, respectively. He visited Nanyang Technological University, Singapore, in 2004, as a Research Fellow. He is currently a Professor with Northeastern University. His current research interests include fault detection and adaptive control. Dr Zhai is an Associate Editor of the International Journal of Fuzzy Systems, International Journal of Control, Automation and Systems and IEEE ACCESS.