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Dissipative stability analysis and control of two-dimensional Fornasini–Marchesini local state-space model

Author

Listed:
  • Lanning Wang
  • Weimin Chen
  • Lizhen Li

Abstract

This paper is concerned with the problems of dissipative stability analysis and control of the two-dimensional (2-D) Fornasini–Marchesini local state-space (FM LSS) model. Based on the characteristics of the system model, a novel definition of 2-D FM LSS (Q, S, R)-α-dissipativity is given first, and then a sufficient condition in terms of linear matrix inequality (LMI) is proposed to guarantee the asymptotical stability and 2-D (Q, S, R)-α-dissipativity of the systems. As its special cases, 2-D passivity performance and 2-D H∞ performance are also discussed. Furthermore, by use of this dissipative stability condition and projection lemma technique, 2-D (Q, S, R)-α-dissipative state-feedback control problem is solved as well. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Suggested Citation

  • Lanning Wang & Weimin Chen & Lizhen Li, 2017. "Dissipative stability analysis and control of two-dimensional Fornasini–Marchesini local state-space model," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(8), pages 1744-1751, June.
    • Handle: RePEc:taf:tsysxx:v:48:y:2017:i:8:p:1744-1751
    DOI: 10.1080/00207721.2017.1282059
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