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New Criterion for l2–l∞ Stability of Interfered Fixed-Point State-Space Digital Filters with Quantization/Overflow Nonlinearities

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Abstract

The problem of l2–l∞ stability and disturbance attenuation performance analysis of fixed-point state-space digital filters with external disturbance and finite wordlength nonlinearities is studied in this paper. The finite wordlength nonlinearities are composite nonlinearities representing concatenations of quantization and overflow correction employed in practice. Using sector-based characterization of the finite wordlength nonlinearities, a new l2–l∞ stability criterion for the reduction of the effects of external disturbance to a given level and to confirm the nonexistence of limit cycles in the absence of external interference is established. Numerical examples are given to illustrate the efficacy of the proposed criterion.

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Acknowledgements

The authors thank the Editors and the anonymous reviewers for their constructive comments and suggestions to improve the manuscript.

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Authors and Affiliations

  1. Department of Electronics and Communication Engineering, Motilal Nehru National Institute of Technology Allahabad, Allahabad, 211004, India

    Pooja Rani & Haranath Kar

  2. Department of Electronics Engineering, Indian Institute of Information Technology Design and Manufacturing, Kancheepuram, Chennai, 600127, India

    Priyanka Kokil

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  1. Pooja Rani
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  2. Priyanka Kokil
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Correspondence to Pooja Rani.

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Rani, P., Kokil, P. & Kar, H. New Criterion for l2–l∞ Stability of Interfered Fixed-Point State-Space Digital Filters with Quantization/Overflow Nonlinearities. Circuits Syst Signal Process 38, 407–424 (2019). https://doi.org/10.1007/s00034-018-0866-9

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