Abstract
This paper is concerned with a Lyapunov stability analysis of a two-dimensional (2-D) discrete-time system described by a high-order partial difference equation in the behavioral setting. We first formulate the autonomy and asymptotic stability of 2-D discrete-time behavior in terms of the characteristic set over Z2. A sufficient condition for asymptotic stability is derived in terms of quadratic difference forms. This condition can be numerically checked by solving a certain four-variable polynomial matrix equation. It also turns out that the present result generalizes some existing stability conditions for the Fornasini-Marchesini state-space model to the behavioral setting.
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