$l_{2}-l_{\infty}$ Suppression of Limit Cycles in Interfered Two-Dimensional Digital Filters: A Fornasini–Marchesini Model Case

Abstract

Recently, Ahn proposed an l 2 -l ∞ stability criterion for interfered two-dimensional (2-D) digital filters described by the Roesser model. However, until now, no criteria for interfered 2-D digital filters in the Fornasini-Marchesini (FM) model have been studied. As a continuation of the results, this brief proposes a new criterion for the l 2 -l ∞ suppression of limit cycles in interfered 2-D digital filters in the FM model. The proposed criterion ensures the asymptotic stability and l 2 -l ∞ performance of 2-D digital filters. The effectiveness of the proposed criterion is demonstrated using numerical examples. The work in this brief and that of the Roesser model provide, as an integrity, systematic results on limit cycle suppression for 2-D digital filters in the l 2 -l ∞ sense.