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Abstract
This paper is concerned with the sampling-interval-dependent stability of linear sampled-data systems with non-uniform sampling. A new Lyapunov-like functional is constructed to derive sampling-interval-dependent stability results. The Lyapunov-like functional has three features. First, it depends on time explicitly. Second, it may be discontinuous at the sampling instants. Third, it is not required to be positive definite between sampling instants. Moreover, the new Lyapunov-like functional can make use of the information fully of the sampled-data system, including that of both ends of the sampling interval. By making a new proposition for the Lyapunov-like functional, a sampling-interval-dependent stability criterion with reduced conservatism is derived. The new sampling-interval-dependent stability criterion is further extended to linear sampled-data systems with polytopic uncertainties. Finally, examples are given to illustrate the reduced conservatism of the stability criteria.
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Hanyong Shao
Hanyong Shao received his MSc degree in operational research and control theory from Qufu Normal University, Qufu, China, and his PhD degree in control theory and engineering from Southeast University, Nanjing, China, in 1997 and 2005, respectively. In 1997, he joined the School of Electrical and Information Automation, Qufu Normal University, Rizhao, Shandong, China, where he is currently a professor. In 2009, he was a research associate in Centre for Intelligent and Networked Systems, Central Queensland University, Australia. In 2013, he was a research associate in the Department of Mechanical Engineering, the University of Hong Kong, Hong Kong. His research interests include sampled-data systems, time-delay systems, neural networks, robust control and its applications.
James Lam
James Lam received his 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 his MPhil and PhD degrees from the University of Cambridge. He is a recipient of the Croucher Foundation Scholarship and Fellowship, the Outstanding Researcher Award of the University of Hong Kong, and the Distinguished Visiting Fellowship 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 held lectureships at the City University of Hong Kong and the University of Melbourne. He 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, section Editor of Cogent Engineering, associate editor of Automatica, International Journal of Systems Science, International Journal of Applied Mathematics and Computer 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. His research interests include model reduction, robust synthesis, delay, singular systems, stochastic systems, multidimensional systems, positive systems, networked control systems and vibration control.
Zhiguang Feng
Zhiguang Feng received his BS degree in automation from Qufu Normal University, Rizhao, China, in 2006, his MS degree in Control Science and Engineering from Harbin Institute of Technology, Harbin, China, in 2009, and his PhD degree in the Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, in 2013. In 2013, he joined the Bohai University, where he is currently an associate professor. From 2013 to 2014, he was a research associate with the Department of Mechanical Engineering, the University of Hong Kong. From 2014 to 2015, he was a visiting fellow with the School of Computing, Engineering and Mathematics, the University of Western Sydney. His research interests include singular systems, time-delay systems, robust control, dissipative control and reachable set estimation.