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IMA Journal of Mathematical Control and Information Advance Access originally published online on June 3, 2005
IMA Journal of Mathematical Control and Information 2005 22(4):441-452; doi:10.1093/imamci/dni036
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© The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

New results on quadratic stabilization of switched linear systems with polytopic uncertainties

Zhijian Ji, Long Wang** and Guangming Xie***

Intelligent Control Laboratory, Center for Systems and Control, Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China

** Corresponding author. Email: longwang{at}pku.edu.cn

*** Email: jizj{at}mech.pku.edu.cn

In this paper, the quadratic stabilization of switched linear systems with polytopic uncertainties is considered. Compared with the existing result, a more general switching control method is proposed to guarantee the quadratic stabilization. This switching control method is based on the partition of the vertex matrix set of each subsystem. By this method, the matrix inequalities needed to be solved are always less than those needed to be solved before except one extreme case; for this case, it is equal. The switched control synthesis problem is also studied for both switched state feedback and output feedback. Several bilinear matrix inequality based conditions are derived for both cases.

Keywords: switched systems; stabilization; feedback; switching law; polytopic-type uncertainty.

Received on 7 June 2004. revised on 23 December 2004. accepted on 23 December 2004.


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