Input-output finite-region stability and stabilization for discrete 2-D Fornasini-Marchesini models

This paper establishes input-output finite-region stability (I-O FRS) and stabilization analysis methods to investigate the transient behavior of output signals for discrete two-dimensional (2-D) Fornasini-Marchesini (FM) models. For 2-D systems with two classes of input signals, by building special recursive formulas, sufficient I-O FRS conditions are formulated in terms of solvability of linear matrix inequalities (LMIs). Furthermore, aiming at designing static state feedback controllers, I-O finite-region stabilization issues are analyzed for the corresponding 2-D systems and sufficient conditions are reported to guarantee I-O FRS of the closed-loop systems. To conclude the paper, we provide some numerical examples to confirm the validity of the proposed methods.