The dynamic behavior of multi-dimensional recursive difference equations in floating point arithmetic

First hyper-quadrant, recursive difference equations, which are implemented in floating point format, are analyzed. The problems of zero-convergence and limit cycles are investigated, and bounds for various types of unstable responses are obtained. The introduced analysis is independent of order, dimensionality and the type of floating point format used, and can be applied to any floating point implementation of an m-D linear system. It is proved that any linearly stable m-D difference equation can be implemented in floating point format with an arbitrarily small error bound if the mantissa and exponent length are sufficiently large