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ISS Criterion for Lipschitz Nonlinear Interfered Fixed-Point Digital Filters with Saturation Overflow Arithmetic

Abstract

In this paper, we study the problem of input-to-state stability (ISS) of Lipschitz nonlinear fixed-point digital filters in a state-space realization with saturation arithmetic and external disturbance. Using the Lyapunov theory along with the ‘passivity property’ of saturation nonlinearities and the Lipschitz condition, a new criterion for the ISS of such digital filters is established. The criterion can be used to confirm the diminishing effect of external interference as well as to guarantee the asymptotic stability of digital filters in the absence of interference. Suitable examples are given to illustrate the efficacy of the proposed approach.

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Data Availability

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

Abbreviations

\({\varvec{R}}^{\mu }\) :

Set of \(\mu \times 1\) real vectors

\({\varvec{R}}^{\mu \times \tau }\) :

Set of \(\mu \times \tau\) real matrices

\({\mathbb{R}}^{ + }\) :

Set of nonnegative real numbers

\({\varvec{\varPi}}^{{{T}}}\) :

Transpose of a vector (or matrix) \({\varvec{\varPi}}\)

\({\mathbf{0}}\) :

Null vector or null matrix of appropriate dimension

\({\varvec{\varPi}} > {\mathbf{0}}\) :

Matrix \({\varvec{\varPi}}\) is symmetric and positive definite

\({\varvec{\varPi}} < {\mathbf{0}}\) :

Matrix \({\varvec{\varPi}}\) is symmetric and negative definite

\(\left\| {\; \cdot \;} \right\|\;\) :

Any vector norm or matrix norm

\(\lambda_{\;\min } ({\varvec{\varPi}})\) :

Minimum eigenvalue of matrix \({\varvec{\varPi}}\)

\(\lambda_{\;\max } ({\varvec{\varPi}})\) :

Maximum eigenvalue of matrix \({\varvec{\varPi}}\)

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Correspondence to Janmejaya Rout.

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Rout, J., Kar, H. ISS Criterion for Lipschitz Nonlinear Interfered Fixed-Point Digital Filters with Saturation Overflow Arithmetic. Circuits Syst Signal Process (2021). https://doi.org/10.1007/s00034-021-01823-5

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Keywords

  • Digital filter
  • External interference
  • Inherent system nonlinearity
  • Input-to-state stability
  • Saturation nonlinearity