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

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.

KEYWORDS:

• Two-dimensional (2-D) systems
• Fornasini–Marchesini local state-space (FM LSS) model
• dissipative stability
• dissipative control

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported in part by the National Natural Science Foundation of China [grant number 61573007]; the Research Fund for the Doctoral Program of Higher Education of China [grant number 20133219110040]; and the Scientific Research Foundation of NUPT [grant number NY215178].