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Strict dissipativity and asymptotic stability of digital filters in direct form with saturation nonlinearity

Abstract

In this paper, we investigate the strict dissipativity and asymptotic stability of digital filters in the direct form with saturation nonlinearity. First, a novel criterion is presented for the (QSR)-\(\alpha \)-dissipativity of single digital filters in the direct form. By selecting the weighting scalar parameters, this condition reduces to the conditions for \(H_{\infty }\), passivity, and mixed \(H_{\infty }\)/passivity performances. Based on this result, a new sufficient criterion is proposed for the (QSR)-\(\alpha \)-dissipativity of interconnected digital filters in the direct form. A condition for the asymptotic stability of interconnected direct-form digital filters is also presented, and three numerical examples are included to show the effectiveness of the developed theoretical results.

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Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2014R1A1A1006101).

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Correspondence to Choon Ki Ahn.

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Ahn, C.K., Shi, P. Strict dissipativity and asymptotic stability of digital filters in direct form with saturation nonlinearity. Nonlinear Dyn 85, 453–461 (2016). https://doi.org/10.1007/s11071-016-2698-0

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  • DOI: https://doi.org/10.1007/s11071-016-2698-0

Keywords

  • Dissipativity
  • Digital filter
  • Direct form
  • Interconnection
  • Stability