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Stability of Digital Filters with State-Delay and External Interference

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Abstract

This work addresses stability of interfered digital filters with state-delay and saturation arithmetic. By utilizing a quadratic Lyapunov functional and properties of saturation overflow, a new condition is established to ensure stability of interfered digital filters under the influence of saturation arithmetic and state-delay. The criterion is capable of finding minimum \(H_\infty \) norm in the existence of external disturbance and ensures exponential stability in the nonexistence of disturbance. Further, an improved condition is obtained to ensure asymptotic stability of digital filters with saturation arithmetic. The established conditions are in linear matrix inequality framework and therefore computationally less demanding. It is shown that the stability criteria presented in this study are less stringent than few existing stability results. With the help of numerical examples, superiority of the presented approach is demonstrated.

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Acknowledgements

The authors are thankful to the Editor and to anonymous reviewers for their constructive comments and suggestions. This work is supported by Department of Atomic Energy, Government of India under Grant No. 02011/6/2019 NBHM(R.P)/R and D II/1615.

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

    C. G. Parthipan & Priyanka Kokil

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  1. C. G. Parthipan
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Parthipan, C.G., Kokil, P. Stability of Digital Filters with State-Delay and External Interference. Circuits Syst Signal Process 40, 3866–3883 (2021). https://doi.org/10.1007/s00034-021-01650-8

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