An LMI approach to minimum sensitivity analysis with application to fault detection

  • Authors:
  • Jian Liu;Jian Liang Wang;Guang-Hong Yang

  • Affiliations:
  • Honeywell International, Olathe, Kansas, USA;School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore;Temasek Laboratories, National University of Singapore, 5 Sports Drive, Singapore 117508, Singapore

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2005

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Abstract

This paper systematically studies the minimum input sensitivity analysis problem. The lowest level of sensitivity of system outputs to system inputs is defined as an H"- index. A full characterization of the H"- index is given, first, in terms of matrix equalities and inequalities, and then in terms of linear matrix inequalities (LMIs), as a dual of the Bounded Real Lemma. A related problem of input observability is also studied, with new necessary and sufficient conditions given, which are necessary for a fault detection system to have a nonzero worst-case fault sensitivity. The above results are applied to the problem of fault detection filter analysis, with numerical examples given to show the effectiveness of the proposed approaches.