A novel LMI-based criterion for the stability of direct-form digital filters utilizing a single two’s complement nonlinearity

A criterion for the global asymptotic stability of direct-form digital filters using two’s complement arithmetic is presented. The criterion is in the form of a linear matrix inequality (LMI) and, hence, computationally tractable. Splitting the two’s complement nonlinearity sector [−1,1] into two smaller sectors, [0, 1] and [−1,0], together with using a type of “generalized” sector condition by involving saturation nonlinearity, is the novel feature in the present proof. A special case of the criterion is highlighted. The effectiveness of the present approach is demonstrated by showing its ability to establish the two’s complement overflow stability region, in the parameter space, for a second-order digital filter.