Practical-BIBO stability of n-dimensional discrete systems

It is shown that the conventional definition of BIBO stability for n-dimensional discrete systems is unnecessarily restrictive for most practical applications. The conventional definition permits the input signal to be unbounded in all n dimensions; however, in most practical applications the input signal is unbounded in, at most, one dimension. Based on this, a new definition of practical-BIBO stability is introduced which is less restrictive, and more relevant for practical applications than the conventional one. It is shown that the voltage transfer function of an n-D continuous network, consisting of a reactance 2-port terminated in a resistance, leads to practical-BIBO stable n-D digital filters after bilinear transformation. An example demonstrates the usefulness of the new definition.