Robust passivity and feedback passification of a class of uncertain fractional-order linear systems

ABSTRACT

Theoretical results on robust passivity and feedback passification of a class of uncertain fractional-order (FO) linear systems are presented in the paper. The system under consideration is subject to time-varying norm-bounded parameter uncertainties in both the state and controlled output matrices. Firstly, some suitable notions of passivity and dissipativity for FO systems are proposed, and the relationship between passivity and stability is obtained. Then, a sufficient condition in the form of linear matrix inequality (LMI) for such system to be robustly passive is given. Based on this condition, the design method of state feedback controller is proposed when the states are available. Moreover, by using matrix singular value decomposition and LMI techniques, the existing condition and method of designing a robust observer-based passive controller for such systems are derived. Numerical simulations demonstrate the effectiveness of the theoretical formulation.

KEYWORDS:

• Fractional-order systems
• passification
• passivity
• uncertain

Acknowledgments

The authors would like to express their deep gratitude to the Editors and the anonymous referees for their helpful comments and suggestions, which have greatly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

YangQuan Chen http://orcid.org/0000-0002-7422-5988

Additional information

Funding

This work was supported by the National Natural Science Funds of China [No. 61403115, No. 11571016, No. 51577046], the Fundamental Research Funds for the Central Universities [Nos. JZ2016HGTB0718; JZ2016HGXJ0022], the State Key Program of National Natural Science Foundation of China [No. 51637004] and the National Key Research and Development plan important scientific instruments and equipment development [No. 2016YFF0102200].

Notes on contributors

Liping Chen

Liping Chen received the B.S. degree in Applied Mathematics from Anhui Normal University, Wuhu, China, the M.S. degree in Basic Mathematics from Anhui University, Hefei, China, and the Ph.D. degree in School of Automation, Chongqing University, Chongqing, China, in 2007, 2010 and 2013, respectively. He is now an associate professor at Hefei University of Technology. His current research interests include the areas of neural networks, fractional-order systems and nonlinear dynamical systems.

Tingting Li

Tingting Li received the B.S. degree in Automation from Anhui University of Technology, Maanshan, China. She is currently pursuing the M.S. degree at the Hefei University of Technology, Hefei, China. His research interests include intelligent optimization algorithm, fractional-order control and power electronics controls.

YangQuan Chen

YangQuan Chen earned his Ph.D. degree in advanced control and instrumentation from Nanyang Technological University, Singapore, in 1998. Dr. Chen was on the faculty of Electrical and Computer Engineering at Utah State University before he joined the School of Engineering, University of California, Merced in 2012 where he teaches “Mechatronics” and “Unmanned Aircraft Systems” for juniors and “Fractional Order Mechanics” and “Nonlinear Control” for graduates. His current research interests include mechatronics for sustainability, MIMO cognitive process control, multi-UAV based cooperative multi- spectral “personal remote sensing” and applications, applied fractional calculus in controls, signal processing and energy informatics; distributed measurement and distributed control of distributed parameter systems using mobile actuator and sensor networks.

Ranchao Wu

Ranchao Wu received the B.S. degree in Applied Mathematics from Anhui Normal University, Wuhu, China, in 1994, and Ph.D. degree in Applied Mathematics from Nanjing University, Nanjing, China, in 2006. He is currently a professor and a doctor adviser at Anhui University. His current research interests include nonlinear dynamic systems, bifurcation and chaos, neural networks, control theory.

Suoliang Ge

Suoliang Ge received the B.S. degree and the M.S. degree in Automation from Hefei University of Technology, Hefei, China, in 1984 and 1989, respectively. He is now an associate professor at Hefei University of Technology. His current research interests include complex systems, nonlinear dynamics, industrial control systems.