Asymptotic Stability of Fixed-Point State-Space Digital Filters with Saturation Arithmetic and External Disturbance: An IOSS Approach

A criterion for the input/output-to-state stability of interfered state-space digital filters with saturation arithmetic and external interference is presented. The proposed linear matrix inequality-based criterion ensures the reduction in the effect of external interference as well as confirms the asymptotic stability in the absence of external interference. The criterion turns out to be an improvement over a previously reported criterion. A numerical example is given to illustrate the applicability of the proposed criterion

An improved criterion for peak-to-peak realization of direct-form interfered digital filters employing saturation nonlinearities

Purpose - The purpose of this paper is to present a criterion for global asymptotic stability of state-space direct-form digital filters employing saturation arithmetic. Design/methodology/approach - 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. Findings - 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. Practical implications - 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. Originality/value - 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