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

Lanning Wang, Weimin Chen and Lizhen Li

International Journal of Systems Science, 2017, vol. 48, issue 8, 1744-1751

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.

Date: 2017
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DOI: 10.1080/00207721.2017.1282059

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