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This paper deals with the problem of input/output-to-state stability (IOSS) of direct-form digital filters, which simultaneously contain external disturbances and two's complement nonlinearity. The nonlinearity under consideration is confined to the sector [–1, 1], which contains saturation, zeroing, two's complement and triangular.

The proposed condition is based on IOSS approach, which is capable of providing a framework for checking and analysing the stability of nonlinear system based on input as well as output information.

A linear matrix inequality (LMI)-based new sufficient criterion for the IOSS of the suggested system is obtained. The obtained criterion is capable of detecting the output-to-state stability (OSS) and asymptotic stability of direct-form digital filters with zero external disturbances. In addition, state-norm estimator for the filter under consideration is constructed by adopting an exponential-decay IOSS criterion. Several examples are provided to illustrate the usefulness of the proposed criteria.

The result of the paper is introduced for the first time, and it is suitable for stability analysis of interfered direct-form digital filter with two's complement overflow using IOSS approach.

The purpose of this paper is to develop a new criterion for the exponential stability and

_∞ performance of state-space digital filters under the influence of any combination of quantization/overflow nonlinearities.

The proposed criterion uses the

_∞ approach that is suitable for the design of discrete system in the presence of external disturbance. Analysis and synthesis in an

_∞ setting is advantageous as it proposes effective disturbance attenuation, less sensitivity to uncertainties and many practical applications.

The criterion not only guarantees exponential stability but also reduces the effect of external interference. A numerical example demonstrating the effectiveness of the proposed method is given.

The main result of the paper is reported for the first time and it is useful to ensure the stability of digital filters in the presence of external disturbance and any combination of quantization/overflow nonlinearities.

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.