Stability of nonconvolutional n-D linear discrete systems

Abstract

Stability of linear discrete shift-invariant n-D systems is often discussed in terms of best-in best-out stability and/or in terms of zeros of certain polynomials. This approach assumes that there exists a sequence h, such that for any input sequence x, the output y can be expressed as y=h/sup */x. The condition h/spl isin//spl lscr/ /sup 1/ then easily yields the desired result. Many linear discrete systems with n>1 (even some of the shift-invariant ones) do not satisfy this basic assumption. Here, such systems are called nonconvolutional. Among others, all systems described by difference equations with variable coefficients belong to this class together with many difference equations with constant coefficients. This paper establishes some sufficient conditions of stability for these nonconvolutional systems. It also yields methods to establish growth estimates of solutions of n-D difference equations.