LMI-based robust sampled-data stabilization of polytopic LTI systems: A truncated power series expansion approach

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• 作者：Dong Hwan Lee (1)
  Young Hoon Joo (2)
  
  1. Department of Electrical and Computer Engineering ; Purdue University ; West Lafayette ; IN ; 47906 ; USA
  2. Department of Control and Robotics Engineering ; Kunsan National University ; Kunsan ; Chonbuk ; 573-701 ; Korea
  
• 关键词：Linear matrix inequality (LMI) ; linear time ; invariant (LTI) systems ; polytopic uncertainty ; sampled ; data control ; truncated power series
• 刊名：International Journal of Control, Automation and Systems
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：13
• 期：2
• 页码：284-291
• 全文大小：1,416 KB
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• 刊物类别：Engineering
• 刊物主题：Control Engineering
  
• 出版者：The Institute of Control, Robotics and Systems Engineers and The Korean Institute of Electrical Engi
• ISSN：2005-4092

文摘

For continuous-time linear time-invariant (LTI) systems with polytopic uncertainties, we develop a robust sampled-data state-feedback control design scheme in terms of linear matrix inequalities (LMIs). Truncated power series expansions are used to approximate a discretized model of the original continuous-time system. The system matrices obtained by using the power series approximations are then expressed as homogeneous polynomial parameter-dependent (HPPD) matrices of finite degrees, and conditions for designing the controller are formulated as a HPPD matrix inequality, which can be solved by means of a recent LMI relaxation technique to test the positivity of HPPD matrices with variables in the simplex. To take care of the errors induced by the remainder terms of the truncated power series, the terms are considered as norm bounded uncertainties and then incorporated into the proposed LMI conditions. Finally, examples are used to illustrate the approach.