Brief paper: Strong γk-γclH∞ stabilization with a new slack variable approach

  • Authors:

  • Peng Cheng;Yong-Yan Cao;Youxian Sun

  • Affiliations:

  • Institute of Industrial Process Control, State Key Laboratory of Industrial Control Technology, Zhejiang University, HangZhou 310027, PR China;Department of Automation, Wuhan University of Science and Technology, Wuhan 430081, PR China;Institute of Industrial Process Control, State Key Laboratory of Industrial Control Technology, Zhejiang University, HangZhou 310027, PR China

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2009

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Abstract

This paper deals with the strong @c"k-@c"c"lH"~ stabilization problem. A new bounded real lemma is provided by adding two slack variables, which provides extra freedom to include more control constraints in handling robust control problems. With the extended bounded real lemma, a new sufficient condition is proposed for nth order strong @c"k-@c"c"lH"~ stabilization. It is also proved that the design of an lxnth order (l=2) strong @c"k-@c"c"lH"~ controller can be transformed into that of an nth order controller for an associated plant, which tackles the possible order problem. Furthermore, the H"~ stable stabilization and strong stabilization problems can also be solved by relaxing certain constraints accordingly. Despite the BMI constraints, the path-following and alternative iteration methods are adopted to propose procedures for both nth and lxnth order controller designs. The effectiveness is indicated by several numerical examples.