2-D BIBO stability using 1-D wave model

The bounded-input, bounded-output (BIBO) stability of 2-D shift-invariant systems is studied using the concept of the wave advance model, which converts the 2-D equation into a 1-D time-varying format. It is shown that the wavefront 1-D discrete Fourier transforms evolve according to a conventional time-invariant equation. The propagation model is used to develop 2-D BIBO stability criteria. The most general criterion is necessary and sufficient for BIBO stability of systems without singularities of the second kind on the unit bidisk. The criteria are sufficient when applied to 2-D systems with singularities of the second kind. In fact, this kind of singularity appears as a loss controllability (pole/zero cancellation) in a related 1-D observable canonical state equation. The approach proposed shows very clearly the effect of the numerator in the stability of such systems. The stability analysis of singularities can be carried out with conventional algebraic tools