An improved criterion for the global asymptotic stability of 2-D state-space digital filters with finite wordlength nonlinearities

• Stability criterion of fixed-point 2-D digital filter with finite wordlength is presented.
• Criterion is based on a more precise characterization of the nonlinearities.
• Criterion is less stringent than several existing criteria.

This paper investigates the problem of global asymptotic stability of fixed-point state-space two-dimensional (2-D) digital filters described by the Roesser model in the presence of finite wordlength nonlinearities. The class of nonlinearities under consideration captures the combined effects of quantization (except value truncation) and overflow arithmetic employed in practice. A new criterion for the limit cycle-free realization of 2-D digital filters is proposed. The criterion is based on a more precise sector-based characterization of the nonlinearities which exploits the information of the wordlength available in the digital processor. The criterion is compared with the previously reported criteria.