H_∞ bounded real lemma for singular fractional-order systems

ABSTRACT

This paper derives the bounded real lemma corresponding to $H_{\mathrm{\infty }}$ norm of the singular fractional-order system (SFOS). The $H_{\mathrm{\infty }}$ bounded real lemma established for both cases of $0<\alpha <1$ and $1<\alpha <2$ has no conservatism and it turns the original complex computation of $H_{\mathrm{\infty }}$ norm into linear matrix inequality (LMI) problem, which can be performed in a computationally efficient fashion. In addition, it can test the system stability automatically, which is critical for system analysis. From this advantage, the synthesis problem of $H_{\mathrm{\infty }}$ control for the SFOS is addressed in the form of LMI. The simulation study is performed to validate the effectiveness and efficiency of the proposed methods.

Keywords:

• $H_{\mathrm{\infty }}$ bounded real lemma
• singular fractional-order systems
• $H_{\mathrm{\infty }}$ control
• linear matrix inequality

Acknowledgments

The work described in this paper was fully supported by the National Natural Science Foundation of China (Nos. 61601431, 61573332), the Anhui Provincial Natural Science Foundation (No. 1708085QF141), the Fundamental Research Funds for the Central Universities (No. WK2100100028), and the General Financial Grant from the China Postdoctoral Science Foundation (No. 2016M602032).

Disclosure statement

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

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

The work described in this paper was fully supported by the National Natural Science Foundation of China [grant number 61601431], [grant number 61573332], the Anhui Provincial Natural Science Foundation [grant number 1708085QF141], the Fundamental Research Funds for the Central Universities [grant number WK2100100028], the General Financial Grant from the China Postdoctoral Science Foundation [grant number 2016M602032] and the fund of China Scholarship Council [grant number 201706340089], [grant number 201806345002].

Notes on contributors

Yuman Li

Yuman Li revieved her B.E. degree in automation from the University of Science and Technology of China, in 2018. She is currently pursuing the Ph.D. degree of Mechanical Engineering at the University of HongKong. Her research interests include fractional order system theory, system robust control, network attack and defense.

Yiheng Wei

YiHeng Wei received his B.E. and Ph.D. degrees from the Northeast University and the University of Science and Technology of China in 2010 and 2015, respectively. He was a postdoctoral fellow of the City University of Hong Kong and the University of Science and Technology of China from 2015 to 2017. He was an Associate Professor of USTC from 2017 to 2020. He is currently a Faculty Member with the School of Mathematics, Southeast University, Nanjing 211189, China. His research interests include fractional-order systems and control, numerical computation, and stochastic learning.

Chen Yuquan

Yuquan Chen received his B.E. and Ph.D. degrees from the Northeast University and the University of Science and Technology of China in 2014 and 2020, respectively. He participated in the Ph.D joint training program between University of Science and Technology of China and University of California, Merced from 2017 to 2019. He is currently a Faculty Member the College of Energy and Electrical Engineering, Hohai University, Nanjing 211106, China. His research interests include fractional order system, nonlinear control and stochastic learning.

Yong Wang

Yong Wang received the B.E. degree in automatic control from University of Science and Technology of China in 1982, the M.E. and Ph.D. degrees in navigation, guidance, and control from the Nanjing Aeronautical Institute. He is currently a full professor in University of Science and Technology of China. He is leading several research groups that focus on vibration control, vehicle control and fractional order system control. Professor Wang is the recipient of the 2013, 2014 and 2015 Chinese Academy of Sciences Outstanding Instructor.