Robust sampled-data H_∞ control of uncertain singularly perturbed systems using time-dependent Lyapunov functionals

Abstract

In this paper, the problem of robust sampled-data H_∞ control of linear uncertain singularly perturbed systems is investigated. The parametric uncertainties are assumed to be time-varying and norm-bounded. Two types of controller design are considered: (1) with a fast sampling in the fast state and a slow one in the slow state, and (2) with a fast sampling in both states. For each type, a time-dependent Lyapunov functional associated with the sampling pattern is introduced to analyse the exponential stability and L₂-gain performance of the closed-loop system. Linear matrix inequalities based solutions of the robust sampled-data H_∞ control problem are derived. The new results are proved theoretically to be less conservative than the existing results. An illustrative example is given which substantiates the usefulness of the proposed method.

Keywords:

• singularly perturbed systems
• sampled-data control
• H_∞ control

Acknowledgements

The authors would like to thank the editor, the associate editor and the three anonymous reviewers for their valuable comments and suggestions which helped to significantly improve the quality and presentation of this paper.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61164016]; the Key Project of Guangxi Natural Science Foundation [grant number 2013GXNSFDA019003]; the Guangxi Natural Science Foundation [grant number 2011GXNSFA018141].

Notes on contributors

Wu-Hua Chen

Wu-Hua Chen received his BSc degree in mathematics from Hubei Normal University, Huangshi, China, his MSc degree in basic mathematics from Guangxi Normal University, Guilin, China, and his PhD degree in control theory and control engineering from Huazhong University of Science and Technology, Wuhan, China, in 1988, 1991 and 2004, respectively. From 1991 to 2001, he was with Guangxi University for Nationalities, Nanning, China. In September 2001, he joined Guangxi University, Nanning, China, where he is currently working as a professor. From April 2005 to October 2005, from July 2007 to January 2008 and from September 2008 to July 2009, he was a visiting fellow in the University of Western Sydney, Australia. His research interests include time-delay systems, robust control, neural networks, impulsive systems and stochastic systems.

Zipeng Wang

Zipeng Wang received his BS degree in mathematics and applied mathematics from Fuyang Normal College, Fuyang, China, and his MS degree in applied mathematics from Guangxi University, Nanning, China, in 2010 and 2013, respectively. He is currently pursuing his PhD degree in control theory and control engineering from Beihang University (Beijing University of Aeronautics and Astronautics), Beijing, China. His research interests include sampled-data control, impulsive control, robust control, and fuzzy modelling and control.

Dan Wei

Dan Wei received her BS degree in mathematics and applied mathematics from Anyang Normal University, Anyang, China, and his MS degree in applied mathematics from Guangxi University, Nanning, China, in 2010 and 2013, respectively. Her research interests include impulsive control systems and fuzzy systems.

Xiaomei Lu

Xiaomei Lu received her BS degree in mathematics from Guangxi Normal University, Guilin, China, in 1991. She is currently an associate professor in the College of Mathematics and Information Science at Guangxi University. Her current research interests include delay differential equations, robust control theory and hybrid dynamic systems.