New criteria for the absence of limit cycles in state-space digital filters with combinations of quantization and overflow nonlinearities

The problem of global asymptotic stability of one-dimensional (1-D) digital filters with any combination of overflow and quantization nonlinearities is addressed. The new criteria, based on previous stability results of digital filters with quantization schemes, are applicable to all arithmetic schemes. The method is applicable to any order state-space realization, independent of the type of nonlinearities. It generates simple conditions that lead to improved criteria concerning the nonexistence of limit cycles in digital filters under finite wordlength effects. Since the formulated method is based on the equivalence between the realizations with and without overflow, it can be used to predict limit cycles in systems with overflow