Abstract
ABSTRACTIn this paper, the concepts of finite-region stability (FRS) and finite-region boundedness (FRB) are formulated for discrete two-dimensional (2D) Fornasini–Marchesini second (FMII) models, and then the analysis methods for FRS and FRB are proposed to investigate the transient behaviour of such discrete 2D FMII models. First, by building special recursive formulas, we develop a sufficient condition which guarantees the FRS of the system under solvable linear matrix inequalities (LMIs) conditions. Next, the FRB problem is addressed for the FMII model with exogenous disturbances and the corresponding criteria and LMIs conditions are reported. Finally, we apply the proposed FRS analysis method to consider the finite-region stabilisation problem of a chemical reactor thermal process, as well as some other numerical examples, to illustrate the validity of the proposed methods.
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