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Robust D stabilization of singular systems with polytopic uncertainties
Received:2008/5/1  Revised:2009/12/7
Keywords:Singular system  Robust D stabilization  Free matrices  LMI region
Fund Project:This work was supported by the National Creative Research Groups Science Foundation of China (No.60721062), the National Natural Science Foundation of China (No.60736021), the National High Technology Research and Development Program of China (863 Program) (No.2008AA042902), and National Natural Science Foundation of China (No.60904011).
AuthorInstitutionE-mail
Jianjun BAI State Key Laboratory of Industrial Control Technology, Institute of Cyber-System and Control, Zhejiang University, Hangzhou Zhejiang 310027, China jjbai@iipc.zju.edu.cn 
Hongye SU State Key Laboratory of Industrial Control Technology, Institute of Cyber-System and Control, Zhejiang University, Hangzhou Zhejiang 310027, China  
Xiaofu JI School of Electrical and Information Engineering, Jiangsu University, Zhenjiang Jiangsu 212013, China  
Jinfeng GAO Institute of Automation, Zhejiang Sci-Tech University, Hangzhou Zhejiang 310018, China  
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Abstract:
      The robust D stabilization problem is considered for singular systems with polytopic uncertainties in this paper. Both the derivative matrix E and the state matrix A are with uncertainties, which were not considered before. First, with the introduction of some free matrices, a necessary and sufficient condition for the singular system to be D stable is proposed, based on which, the robust D stable problem is solved, and a sufficient condition for the closed system to be robust D stabilizable is obtained. The desired state feedback controller is given in an explicit expression. Numerical examples show the efficiency of the proposed approach.
Jianjun BAI,Hongye SU,Xiaofu JI and Jinfeng GAO.Robust D stabilization of singular systems with polytopic uncertainties[J].Journal of Control Theory and Applications,2010,8(4):540~544.
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