Stability and performance analysis of switched linear systems subject to time delays and actuator saturation

ABSTRACT

This paper is devoted to the stability and the performance for the switched linear systems with time delays and actuator saturation. Problems to be considered include the reachable set under a class of bounded energy disturbances and time delays. This treatment yields two forms of differential inclusions, a polytopic differential inclusion (PDI) and a norm-bounded differential inclusion (NDI) that contain the original system. Using the PDI and the NDI describing actuator saturation systems, sufficient conditions for the output feedback control laws are derived to stabilise the systems. The estimation of the attraction domain is to ensure that the state remains inside the level set of a certain Lyapunov function where the PDI and NDI are valid. The sufficient conditions for stability and performances are derived as linear matrix inequalities. A example based on jitterbug tools is used to illustrate the effectiveness of the proposed approach.

KEYWORDS:

• Stability
• PDI
• NDI
• saturation
• time delays

ORCID

Yudan Cai http://orcid.org/0000-0002-4783-3822

Additional information

Notes on contributors

Yiwei Feng

Yiwei Feng was born in 1973. He received his Master degree in Control Theory and Control Engineering from the Lanzhou University of Technology in 2007. He received his PhD in Control Theory and Control Engineering from Dalian Maritime University in 2011. His research interests include time-delay systems, networked quantised control systems and multi-agent systems and applications to energy and automotive.

Yudan Cai

Yudan Cai was born in 1993. She is a master degree candidate in Lanzhou University of Technology. Her research interests include Switched control systems, time-delay systems and stability theory.