A computer-aided test for global asymptotic stability of digital filters

The problem of determining the existence of limit cycles in direct form digital filters with quantization nonlinearities under zero-input conditions is considered. A method based on an exhaustive search is introduced. It is independent of the number or the type of quantizers and is applicable to filters of any order. The advantage of this algorithm over previous methods is its ability to always determine the stability or instability of a particular realization. The method was implemented for second-order direct form digital filters. Significant improvements over previous results were obtained for the following cases of quantization schemes: one two´s complement truncation quantizer and two two´s complement truncation quantizers