Stability of 2-D periodic state-space filters

The stability of two-dimensional (2-D) periodically shift varying (PSV) filters formulated as the Givone-Roesser (GR) model is considered. The GR model is embedded into the 2^nd model of Fornasini-Marchesisni (FM) and the stability of this embedded model is then studied. Several sufficient conditions and one necessary condition are obtained.