Exponential stability of singularly perturbed systems with time delay and uncertainties

Abstract

Recently, there are several studies on singularly perturbed systems with time delay and uncertainties. However, the existing results show only the limited results on either time delay or uncertainties. For time delay, small time delay or time delay only on the slow state are considered while, for uncertainties, the uncertain linear singularly perturbed system or the uncertain nonlinear singularly perturbed system with the conservative condition on uncertainties are considered. In this paper, the exponential stability of singularly perturbed systems with both time delay and uncertainties is investigated in the general form.

Keywords:

• singular perturbation
• time delay
• uncertainty
• exponential stability

Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0024161).

Additional information

Notes on contributors

Kyung-In Kang

Kyung-In Kang received the BS degree from the Department of Physics, Kyungpook National University, Korea in 1991, the MS degree from the Department of Engineering, ICU (Information Communications University) in 2001, the MS degree from the Department of Electrical Engineering, KAIST (Korea Advanced Institute of Science and Technology) in 2006 and is currently working towards the PhD degree in the Department of Electrical Engineering, KAIST. His research interests are in the nonlinear control problems with emphasis on feedback linearisation, singular perturbation and output feedback.

Kyun-Sang Park

Kyun-Sang Park received the BS degree from Electronics Engineering, Ajou University in 2006, the MS degree from Graduate School of Automobile Technology, KAIST in 2008, and the PhD degree from the Department of Electrical Engineering, KAIST in 2012. He is currently a senior research engineer in Hyundai Motor Company. His research interests are in the nonlinear control theory, singular perturbation and vehicle dynamics control.

Jong-Tae Lim

Jong-Tae Lim received the BSEE degree from Yonsei University, Seoul, Korea, in 1975, the MSEE degree from the Illinois Institute of Technology, Chicago, in 1983, and the PhD degree in Computer, Information and Control Engineering from the University of Michigan, Ann Arbor, in 1986. He is currently a Professor in the Department of Electrical Engineering, KAIST. His research interests are in the areas of systems and control theory, communication network and discrete event systems. He is a member of IEEE, IEICE and ICROS.