Absolute response error bounds for floating point digital filters in state space representation

The dynamic behavior of state space models for linear systems under the influence of floating point quantization is investigated. Using a previously developed method, tight bounds on the limit cycle amplitudes in each state are derived. It is shown that by using a very small number of mantissa bits for many systems limit cycles occur only in underflow conditions. The results confirm previous knowledge obtained from direct form filters that limit cycles in any linearly stable system implemented in floating point arithmetic can be made arbitrarily small by choosing a sufficiently large mantissa and exponent register length. The analysis also show that the quantization and reformatting scheme have little effect on the derived error bounds