Criterion for the limit cycle free state-space digital filters with external disturbances and quantization/overflow nonlinearities

Abstract

Purpose – The purpose of this paper is to develop a new criterion for the exponential stability and H ∞ performance of state-space digital filters under the influence of any combination of quantization/overflow nonlinearities. Design/methodology/approach – The proposed criterion uses the H ∞ approach that is suitable for the design of discrete system in the presence of external disturbance. Analysis and synthesis in an H ∞ setting is advantageous as it proposes effective disturbance attenuation, less sensitivity to uncertainties and many practical applications. Findings – 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. Originality/value – 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.