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The purpose of this paper is to present a criterion for global asymptotic stability of state-space direct-form digital filters employing saturation arithmetic.

An elegant use of induced l _∞ approach (also known as a peak-to-peak approach) is made to develop a criterion for the overflow stability of state-space direct-form digital filters.

The criterion not only guarantees asymptotic stability but also reduces the effect of external interference. The presented method yields better interference attenuation level as compared to a recently reported method. Numerical examples are given to illustrate the effectiveness of the proposed method.

Digital filters are important dynamical systems in signal processing which are used for the processing of discrete signals. During the implementation of higher-order digital filter in hardware or software, introduction of external interference is unavoidable. Therefore, stability analysis of digital filters in the presence of external interference is of much practical importance.

The main result of the paper is reported for the first time and it is useful to establish the asymptotic stability of digital filters in the presence of external disturbances.