Design of switched linear control systems based on Youla parameterization with average dwell time

ABSTRACT

A two-steps method of designing switched linear systems is presented with the parameterization of globally uniformly asymptotically stabilising controllers with average dwell time (ADT). First, an observer-based switching controller design is given for a class of switched linear system. Based on the construction of observer-based controller, conceptions of doubly coprime factorization and Youla parameterization of LTI systems are extended to switched linear systems with respect to globally uniformly asymptotical stability (GUAS) using a state-space expression. Second, the parameterization of closed-loop systems, which are affine with any globally uniformly asymptotically stable $Q$-parameter, is then described. This description enables the application of the $Q$ –- parameter approach to a variety of switched linear control-system designs. The control construction provides us a two-steps process design procedure. Above all, based on the Schur complementary lemma and controller variable elimination method, a systematic weighted L2 performance strategy is focused on and a design scheme of $Q$ to obtain weighted L2-gain performance is clarified. Finally, a numerical example is given to show the validity and potential of the developed results.

KEYWORDS:

• Observer-based controller
• Youla parameterization
• switching control
• average dwell time

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by YangFan Innovative & Entepreneurial Research Team Project of Guangdong Province [2016YT03G125]; National Nature Science Foundation of China [61803161]; Natural Science Foundation of Guangdong Province [2017A030313385, 2018A030310371]; Science and Technology planning Project of Guangdong Province [2017B090914001; 2017A040403064; 2017B090901040; 2017B030306017; 2017A040405023]; Innovative Research Team Project of Jiangmen [2017TD03].

Notes on contributors

Wei Xie

Prof. Wei Xie was born on 2 September 1974. He received the B.Eng. and M.Eng. degrees from Wuhan University of Science and Technology, China, in 1996 and in 1999, respectively, and the Ph.D. degree in system engineering from the Kitami Institute of Technology, Hokkaido, Japan, in 2003. He has been a Professor in the College of Automation Science and Technology, South China University of Technology, Guangzhou, China since 2010. He was a Postdoctoral Research Fellow at Satellite Venture Business Laboratory, Kitami Institute of Technology (May 2003–June 2006). His current research interests are robust control, fuzzy control and adaptive control.