Robust stability of positive switched systems with dwell time

Abstract

This paper studies robust stability of positive switched systems (PSSs) with polytopic uncertainties in both discrete-time and continuous-time contexts. By using multiple linear copositive Lyapunov functions, a sufficient condition for stability of PSSs with dwell time is addressed. Being different from time-invariant multiple linear copositive Lyapunov functions, the Lyapunov functions constructed in this paper are time-varying during the dwell time and time-invariant afterwards. Then, robust stability of PSSs with polytopic uncertainties is solved. All conditions are solvable via linear programming. Finally, illustrative examples are given to demonstrate the validity of the proposed results.

Keywords:

• positive switched systems
• robust stability
• multiple linear copositive Lyapunov functions
• polytopic uncertainties
• linear programming

Acknowledgements

The authors would like to express their great appreciation to the anonymous reviewers for the valuable comments and suggestions

Additional information

Funding

This work was supported by the National Natural Science Foundation of the People's Republic of China [grant number 11190015], [grant number 61374006].

Notes on contributors

Jinjin Liu

Jinjin Liu received her BS degree from Anyang Normal University in 2008 and MS degree from Henan Normal University in 2011. She is currently a PhD candidate in control theory and control engineering at Southeast University. Her research interests include switched systems and positive systems.

Kanjian Zhang

Kanjian Zhang received his BS degree in mathematics from Nankai University, China in 1994, and his MS and PhD degrees in control theory and control engineering from Southeast University, China in 1997 and 2000, respectively. He is currently a professor in the Research Institute of Automation, Southeast University. His research is in nonlinear control theory and its applications, with particular interest in robust output feedback design and optimization control.

Haikun Wei

Haikun Wei received his BS degree in the Department of Automation, North China University of Technology, China in 1994, and his MS and PhD degrees in the Research Institute of Automation, Southeast University, China in 1997 and 2000, respectively. He was a visiting scholar in RIKEN Brain Science Institute, Japan from 2005 to 2007. His research interests include real and artificial in neural networks and industry automation.