An asymptotically exact LMI solution to the robust discretisation of LTI systems with polytopic uncertainties and its application to sampled-data control

Abstract

In this paper, the problem of robust discretisation of linear time-invariant (LTI) systems with polytopic uncertainties is introduced. More specifically, the main objective is to provide a systematic way to find an approximate discrete-time (DT) model of a continuous-time (CT) plant with uncertainties in polytopic domain. The system matrices of polytopic DT model to be found are expressed as parameter-dependent matrices which are homogeneous polynomials of arbitrary degree with respect to the uncertain variables in the simplex, and is obtained in such a way that the norm between the system matrices and the truncated power series of the exact DT model is minimised while preserving the polytopic structure of the original CT plant. The solution procedures proposed are presented in terms of single-parameter minimisation problems subject to linear matrix inequality (LMI) constraints which are numerically tractable via LMI solvers. Finally, examples are given to show the validity and effectiveness of the proposed techniques.

Keywords:

• discrete-time LTI systems
• polytopic uncertainty
• linear matrix inequality (LMI)
• discretisation
• sampled-date control

Acknowledgements

The authors would like to thank the associate editor and the anonymous reviewers for their careful reading and constructive suggestions.

Additional information

Funding

This work was supported by the National Research Foundation of Korea (NRF) grant, funded by the Korea government, Ministry of Education, Science and Technology (MEST) [grant number NRF-2012R1A2A2A01014088] and the Human Resources Development program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Knowledge Economy [grant number 20124010203240].

Notes on contributors

Dong Hwan Lee

Dong Hwan Lee received the BS degree from the Department of Electronics Engineering, Konkuk University, Seoul, Korea, in 2008, and the MS degree from the Department of Electrical and Electronic Engineering, Yonsei University, Seoul, Korea, in 2010. His current research interests include stability analysis in fuzzy systems, fuzzy-model-based control, and robust control of uncertain linear systems.

Young Hoon Joo

Young Hoon Joo received the BS, MS, and PhD degrees in Electrical Engineering from Yonsei University, Seoul, Korea, in 1982, 1984, and 1995, respectively. He worked with Samsung Electronics Company, Seoul, Korea, from 1986 to 1995, as a project manager. He was with the University of Houston, Houston, TX, from 1998 to 1999, as a visiting professor in the Department of Electrical and Computer Engineering. He is currently a professor in the Department of Control and Robotics Engineering, Kunsan National University, Kunsan, Korea. His major interest is mainly in the field of intelligent robot, intelligent control, human–robot interaction, and intelligent surveillance systems. He served as president for Korea Institute of Intelligent Systems (2008–2009) and is serving as editor-in-chief for International Journal of Control, Automation and Systems (2014–present) and the vice president for the Korean Institute of Electrical Engineers (2013–present).

Myung Hwan Tak

Myung Hwan Tak received the BS and MS degrees in the School of Electronics and Information Engineering from Kunsan National University, Kunsan, Korea, in 2009 and 2011, respectively. He is currently working toward a PhD degree in the School of Electronics and Information Engineering from Kunsan National University, Kunsan, Korea. His research interests include intelligent robot, swarm robot, robot vision, and human–robot interaction.