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H Infinite Stabilization of Uncertain Piecewise Linear Systems with Filippov Solutions

Authors
  • Mohamadreza Ahmadi

    Department of Electrical Engineering, Faculty of Engineering, University of Guilan, Rasht, Iran, P.O. Box: 41635-3756, Postal Code: 41996-13769, Tel: +98 131 6690270, Fax: +98 131 6690271

  • Hamed Mojallali

    Department of Electrical Engineering, Faculty of Engineering, University of Guilan, Rasht, Iran, P.O. Box: 41635-3756, Postal Code: 41996-13769, Tel: +98 131 6690270, Fax: +98 131 6690271

  • Rafael Wisniewski

    Department of Electronic Systems, Automation and Control, Aalborg University, Fredrik Bajers Vej 7 C, 9220, Aalborg East, Denmark, Tel: +45 9940 8762, Fax: +45 9815 1739

Abstract
This paper is concerned with robust stabilization and H infinite control of piecewise linear switched systems subject to uncertainty in the context of Filippov solutions. The analysis developed here encapsulates solutions with infinite switching in finite time. First, a set of linear matrix inequalities are brought forward which determines suficient conditions to investigate the asymptotic stability of Filippov solutions. Then, a method to construct robust stabilizing switching controllers is proposed. Subsequently, the latter result is extended to switching controllers with H infinite performance. The suggested controller synthesis schemes are based on solving sets of bilinear matrix inequalities for which appropriate algorithms are delineated.
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Published
2012-06-29
Section
Articles