H_∞ control problem of linear periodic piecewise time-delay systems

ABSTRACT

This paper investigates the H_∞ control problem based on exponential stability and weighted L₂-gain analyses for a class of continuous-time linear periodic piecewise systems with time delay. A periodic piecewise Lyapunov–Krasovskii functional is developed by integrating a discontinuous time-varying matrix function with two global terms. By applying the improved constraints to the stability and L₂-gain analyses, sufficient delay-dependent exponential stability and weighted L₂-gain criteria are proposed for the periodic piecewise time-delay system. Based on these analyses, an H_∞ control scheme is designed under the considerations of periodic state feedback control input and iterative optimisation. Finally, numerical examples are presented to illustrate the effectiveness of our proposed conditions.

KEYWORDS:

• Exponential stability
• H_∞ control
• periodic piecewise systems
• time delay

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by GRF HKU [grant number 17205815]; National Natural Science Foundation of China [grant number 61703111].

Notes on contributors

Xiaochen Xie

Xiaochen Xie received the B.E. degree in Automation and the M.E. degree in Control Science and Engineering from Harbin Institute of Technology, Harbin, China, in 2012 and 2014, respectively. She is currently working toward the Ph.D. degree in Mechanical Engineering at The University of Hong Kong, Pokfulam, Hong Kong. Her research interests include robust control, periodic systems, switched systems, and process monitoring.

James Lam

James Lam received a BSc (1st Hons.) degree in Mechanical Engineering from the University of Manchester, and was awarded the Ashbury Scholarship, the A.H. Gibson Prize, and the H. Wright Baker Prize for his academic performance. He obtained the MPhil and PhD degrees from the University of Cambridge. He is a Croucher Scholar, Croucher Fellow, and Distinguished Visiting Fellow of the Royal Academy of Engineering. Prior to joining the University of Hong Kong in 1993 where he is now Chair Professor of Control Engineering, he was lecturer at the City University of Hong Kong and the University of Melbourne.

Professor Lam is a Chartered Mathematician, Chartered Scientist, Chartered Engineer, Fellow of Institute of Electrical and Electronic Engineers, Fellow of Institution of Engineering and Technology, Fellow of Institute of Mathematics and Its Applications, and Fellow of Institution of Mechanical Engineers. He is Editor-in-Chief of IET Control Theory and Applications and Journal of The Franklin Institute, Subject Editor of Journal of Sound and Vibration, Editor of Asian Journal of Control, Senior Editor of Cogent Engineering, Associate Editor of Automatica, International Journal of Systems Science, Multidimensional Systems and Signal Processing, and Proc. IMechE Part I: Journal of Systems and Control Engineering. He is a member of the IFAC Technical Committee on Networked Systems, and Engineering Panel (Joint Research Schemes), Research Grant Council, HKSAR. His research interests include model reduction, robust synthesis, delay, singular systems, stochastic systems, multidimensional systems, positive systems, networked control systems and vibration control. He is a Highly Cited Researcher in Engineering (2014, 2015, 2016, 2017) and Computer Science (2015).

Panshuo Li

Panshuo Li received her B.S. and M.S. degrees in Mechanical Engineering from Donghua University and Shanghai Jiao Tong University, Shanghai, China, in 2009 and 2012, respectively. She obtained her Ph.D. degree in Mechanical Engineering from The University of Hong Kong in 2016. Since 2016 she is an Associate Professor in the School of Automation Engineering, Guangdong University of Technology, Guangzhou, China. Her current research interests include switched systems, periodic systems, intelligent vehicle control, and vibration control.