Strictly Positive Real Control for DOSs with a Low Frequency Range

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• 作者：Hongjiu Yang (1) yanghongjiu@126.com
  Yuanqing Xia (2) xia_yuanqing@bit.edu.cn
  Peng Shi (3) Pengshiuk@gmail.com
  Ling Zhao (4) zhaoling84@gmail.com
• 刊名：Lecture Notes in Control and Information Sciences
• 出版年：2012
• 出版时间：2012
• 年：2012
• 卷：430
• 期：1
• 页码：121-133
• 全文大小：388.2 KB
• 作者单位：1. Institute of Electrical Engineering, Yanshan University, Hebei Avenue 438, 066004 Qinhuangdao, China, People鈥檚 Republic2. School of Automation, Beijing Institute of Technology, 100081 Beijing, China, People鈥檚 Republic3. Department of Computing and Mathematical Sciences, University of Glamorgan, CF37 1DL Pontypridd, United Kingdom4. College of Mechanical Engineering, Yanshan University, Qinhuangdao, China, People鈥檚 Republic
• 刊物类别：Engineering
• 刊物主题：Control Engineering
  Vibration, Dynamical Systems and Control
  
• 出版者：Springer Berlin / Heidelberg

文摘

It is well known that each design specification is often given not for the entire frequency range but rather for a low frequency range of relevance, for example a closed-loop shaping control design typically requiring small sensitivity. Weighting method has been proven useful to deal with the finite frequency requirements [150]. However, the additional weights tend to increase the system complexity and the process of selecting appropriate weights is tedious and time-consuming. Another alternative approach has also been used to grid the frequency axis [286], but it suffers from the lack of a rigorous performance guarantee in the design process. Different from weighting function and frequency gridding methods, a generalized KYP lemma has been proposed in [119]. It can avoid computational burden and guarantee gain property performances simultaneously [115]. There are several results in the literature along this line, see for example [114, 116, 117]. Since the notion of positive realness plays a central role in systems theory [3], many researchers have considered positive real control for linear systems such as in [161, 162, 270], and references therein. The finite frequency positive realness approach for dynamical system design from a control perspective has been given in [118].