Stability of a time-varying 2-D state-space digital filter

The problem of establishing sufficient conditions for a time-varying 2-D Givone-Roesser model is studied. The analysis shows that the Lyapunov condition used to guarantee stability of 1-D state-space systems is useful for this problem, but not applicable in a straightforward manner. The elimination of coupling in one of the two directions between the horizontal and vertical state vectors of the Givone-Roesser model does complement the Lyapunov approach such that BIBO stability is achieved.