Stability of 2-D periodically shift variant filters

The stability of two-dimensional (2-D) periodically shift varying (PSV) filters is considered. The considered system is represented in state space by the first model of Fornasini-Marchesini (FM) with periodic coefficients. The stability of this model is then studied. Two necessary conditions and two sufficient conditions are established for asymptotic stability. The conditions are easy to use and computationally simple.