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A New Realizability Condition for Fixed-Point State-Space Interfered Digital Filters Using Any Combination of Overflow and Quantization Nonlinearities

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Abstract

A linear matrix inequality-based new criterion for the input-to-state stability of fixed-point state-space digital filters in the presence of quantization/overflow nonlinearities and external interference is presented. The presented criterion ensures the reduction in the effect of external interference as well as guarantees the asymptotic stability of digital filters without external interference. Some examples highlighting the effectiveness of the presented approach are provided.

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References

  1. N. Agarwal, H. Kar, An improved criterion for the global asymptotic stability of fixed-point state-space digital filters with combinations of quantization and overflow. Digit. Signal Process. 28, 136–143 (2014)

    Article  Google Scholar 

  2. C.K. Ahn, Criterion for the elimination of overflow oscillations in fixed-point digital filters with saturation arithmetic and external disturbance. AEU Int. J. Electron. Commun. 65(9), 750–752 (2011)

    Article  Google Scholar 

  3. C.K. Ahn, A new condition for the elimination of overflow oscillations in direct form digital filters. Int. J. Electron. 99(11), 1581–1588 (2012)

    Article  MathSciNet  Google Scholar 

  4. C.K. Ahn, IOSS criterion for the absence of limit cycles in interfered digital filters employing saturation overflow arithmetic. Circuits Syst. Signal Process. 32(3), 1433–1441 (2013)

    Article  MathSciNet  Google Scholar 

  5. C.K. Ahn, \(l_2 -l_\infty \) elimination of overflow oscillations in 2-D digital filters described by Roesser model with external interference. IEEE Trans. Circuits Syst. II 60(6), 361–365 (2013)

    Article  Google Scholar 

  6. C.K. Ahn, \(l_2 -l_\infty \) stability criterion for fixed-point state-space digital filters with saturation nonlinearity. Int. J. Electron. 100(9), 1309–1316 (2013)

    Article  Google Scholar 

  7. C.K. Ahn, Two new criteria for the realization of interfered digital filters utilizing saturation overflow nonlinearity. Signal Process. 95, 171–176 (2014)

    Article  Google Scholar 

  8. C.K. Ahn, \(l_2 -l_\infty \) suppression of limit cycles in interfered two-dimensional digital filters: a Fornasini–Marchesini model case. IEEE Trans. Circuits Syst. II 61(8), 614–618 (2014)

    Article  Google Scholar 

  9. C.K. Ahn, Some new results on the stability of direct-form digital filters with finite wordlength nonlinearities. Signal Process. 108, 549–557 (2015)

    Article  Google Scholar 

  10. C.K. Ahn, Y.S. Lee, Induced \(l_\infty \) stability of fixed-point digital filters without overflow oscillations and instability due to finite word length effects. Adv. Differ. Equ. 2012(51), 1–7 (2012)

    MathSciNet  MATH  Google Scholar 

  11. C.K. Ahn, P. Shi, Dissipativity analysis for fixed-point interfered digital filters. Signal Process. 109, 148–153 (2015)

    Article  Google Scholar 

  12. C.K. Ahn, P. Shi, Generalized dissipativity analysis of digital filters with finite-wordlength arithmetic. IEEE Trans. Circuits Syst. II 63(4), 386–390 (2016)

    Article  Google Scholar 

  13. C.K. Ahn, P. Shi, M.V. Basin, Two-dimensional dissipative control and filtering for Roesser model. IEEE Trans. Autom. Control 60(7), 1745–1759 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  14. C.K. Ahn, P. Shi, H.R. Karimi, Novel results on generalized dissipativity of 2-D digital filters. IEEE Trans. Circuits Syst. II 63(9), 893–897 (2016)

    Article  Google Scholar 

  15. C.K. Ahn, L. Wu, P. Shi, Stochastic stability analysis for 2-D Roesser systems with multiplicative noise. Automatica 69, 356–363 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  16. P. Bauer, T. Bose, D.P. Brown, Comments on “limit cycles due to roundoff in state-space digital filters” [with reply]. IEEE Trans. Signal Process. 39(4), 955–956 (1991)

    Article  Google Scholar 

  17. T. Bose, Asymptotic stability of two-dimensional digital filters under quantization. IEEE Trans. Signal Process. 42(5), 1172–1177 (1994)

    Article  Google Scholar 

  18. T. Bose, Combined effects of overflow and quantization in fixed-point digital filters. Digit. Signal Process. 4(4), 239–244 (1994)

    Article  Google Scholar 

  19. T. Bose, D. Brown, Zero-input limit cycles due to rounding in digital filters. IEEE Trans. Circuits Syst. 36(6), 931–933 (1989)

    Article  Google Scholar 

  20. T. Bose, D.P. Brown, Limit cycles due to roundoff in state-space digital filters. IEEE Trans. Acoust. Speech Signal Process. 38(8), 1460–1462 (1990)

    Article  Google Scholar 

  21. T. Bose, M.-Q. Chen, Overflow oscillations in state-space digital filters. IEEE Trans. Circuits Syst. 38(7), 807–810 (1991)

    Article  Google Scholar 

  22. T. Bose, M.-Q. Chen, Stability of digital filters implemented with two’s complement truncation quantization. IEEE Trans. Signal Process. 40(1), 24–31 (1992)

    Article  MATH  Google Scholar 

  23. H.J. Butterweck, J.H.F. Ritzerfeld, M.J. Werter, Finite wordlength effects in digital filters: a review. EUT report 88-E-205 (Eindhoven University of Technology, Eindhoven, 1988)

  24. T.A.C.M. Claasen, W.F.G. Mecklenbräuker, J.B.H. Peek, Second-order digital filter with only one magnitude-truncation quantiser and having practically no limit cycles. Electron. Lett. 9(22), 531–532 (1973)

    Article  Google Scholar 

  25. T.A.C.M. Claasen, W.F.G. Mecklenbräuker, J.B.H. Peek, Effects of quantization and overflow in recursive digital filters. IEEE Trans. Acoust. Speech Signal Process. 24(6), 517–529 (1976)

    Article  MathSciNet  Google Scholar 

  26. Diksha, P. Kokil, H. Kar, Criterion for the limit cycle free state-space digital filters with external disturbances and quantization/overflow nonlinearities. Eng. Comput. 33(1), 64–73 (2016)

  27. S. Huang, M.R. James, D. NešIć, P.M. Dower, Analysis of input-to-state stability for discrete time nonlinear systems via dynamic programming. Automatica 41(12), 2055–2065 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  28. Z.-P. Jiang, Y. Wang, Input-to-state stability for discrete-time nonlinear systems. Automatica 37(6), 857–869 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  29. H. Kar, Asymptotic stability of fixed-point state-space digital filters with combinations of quantization and overflow nonlinearities. Signal Process. 91(11), 2667–2670 (2011)

    Article  MATH  Google Scholar 

  30. H. Kar, V. Singh, A new criterion for the overflow stability of second-order state-space digital filters using saturation arithmetic. IEEE Trans. Circuits Syst. I 45(3), 311–313 (1998)

    Article  Google Scholar 

  31. H. Kar, V. Singh, Stability analysis of 1-D and 2-D fixed-point state-space digital filters using any combination of overflow and quantization nonlinearities. IEEE Trans. Signal Process. 49(5), 1097–1105 (2001)

    Article  Google Scholar 

  32. H. Kar, V. Singh, Elimination of overflow oscillations in fixed-point state-space digital filters with saturation arithmetic: an LMI approach. IEEE Trans. Circuits Syst. II 51(1), 40–42 (2004)

    Article  Google Scholar 

  33. H. Kar, V. Singh, Elimination of overflow oscillations in digital filters employing saturation arithmetic. Digit. Signal Process. 15(6), 536–544 (2005)

    Article  Google Scholar 

  34. P. Kokil, A. Dey, H. Kar, Stability of 2-D digital filters described by the Roesser model using any combination of quantization and overflow nonlinearities. Signal Process. 92(12), 2874–2880 (2012)

    Article  Google Scholar 

  35. P. Kokil, V.K.R. Kandanvli, H. Kar, Delay-dependent LMI condition for global asymptotic stability of discrete-time systems with time-varying delay subject to partial state saturation nonlinearities. Mediterr. J. Meas. Control 8(4), 467–476 (2012)

    Google Scholar 

  36. P. Kokil, V.K.R. Kandanvli, H. Kar, A note on the criterion for the elimination of overflow oscillations in fixed-point digital filters with saturation arithmetic and external disturbance. AEU Int. J. Electron. Commun. 66(9), 780–783 (2012)

    Article  Google Scholar 

  37. P. Kokil, H. Kar, An improved criterion for the global asymptotic stability of fixed-point state-space digital filters with saturation arithmetic. Digit. Signal Process. 22(6), 1063–1067 (2012)

    Article  MathSciNet  Google Scholar 

  38. P. Kokil, S.S. Shinde, Asymptotic stability of fixed-point state-space digital filters with saturation arithmetic and external disturbance: an IOSS approach. Circuits Syst. Signal Process. 34(12), 3965–3977 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  39. L.-J. Leclerc, P.H. Bauer, New criteria for asymptotic stability of one-and multidimensional state-space digital filters in fixed-point arithmetic. IEEE Trans. Signal Process. 42(1), 46–53 (1994)

    Article  Google Scholar 

  40. A. Lepschy, G.A. Mian, U. Viaro, A contribution to the stability analysis of second-order direct-form digital filters with magnitude truncation. IEEE Trans. Acoust. Speech Signal Process. 35(8), 1207–1210 (1987)

    Article  Google Scholar 

  41. D. Liu, A.N. Michel, Asymptotic stability of discrete-time systems with saturation nonlinearities with applications to digital filters. IEEE Trans. Circuits Syst. I 39(10), 798–807 (1992)

    Article  MATH  Google Scholar 

  42. J. Löfberg, YALMIP: a toolbox for modeling and optimization in MATLAB. in: Proceedings of the 2004 IEEE International Symposium on CACSD, Taipei, Taiwan, 2–4 Sept 2004, pp. 284–289

  43. J. Monteiro, R.V. Leuken, Integrated Circuit and System Design: Power and Timing Modeling, Optimization and Simulation (Springer, Berlin, 2010)

    Book  Google Scholar 

  44. N. Noroozi, A. Khayatian, S. Ahmadizadeh, H. Karimi, On integral input-to-state stability for a feedback interconnection of parameterised discrete-time systems. Int. J. Syst. Sci. 47(7), 1598–1614 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  45. I.W. Sandberg, The zero-input response of digital filters using saturation arithmetic. IEEE Trans. Circuits Syst. 26(11), 911–915 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  46. P.K. Sim, K.K. Pang, Design criterion for zero-input asymptotic overflow-stability of recursive digital filters in the presence of quantization. Circuits Syst. Signal Process. 4(4), 485–502 (1985)

    Article  MATH  Google Scholar 

  47. E.D. Sontag, Smooth stabilization implies coprime factorization. IEEE Trans. Autom. Control 34(4), 435–443 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  48. J.F. Sturm, Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw. 11(1–4), 625–653 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  49. A.R. Teel, J.P. Hespanha, A. Subbaraman, Equivalent characterizations of input-to-state stability for stochastic discrete-time systems. IEEE Trans. Autom. Control 59(2), 516–522 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  50. Y. Tsividis, Mixed Analog-Digital VLSI Devices and Technology (World Scientific Publishing, Singapore, 2002)

    Book  Google Scholar 

  51. P. Zhao, Y. Zhao, R. Guo, Input-to-state stability for discrete-time stochastic nonlinear systems, in: Proceedings of the 34th Chinese Control Conference, Hefei, China, 28–30 July 2015, pp. 1799–1803

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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

    Mani Kant Kumar & 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. Mani Kant Kumar
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Correspondence to Mani Kant Kumar.

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Kumar, M.K., Kokil, P. & Kar, H. A New Realizability Condition for Fixed-Point State-Space Interfered Digital Filters Using Any Combination of Overflow and Quantization Nonlinearities. Circuits Syst Signal Process 36, 3289–3302 (2017). https://doi.org/10.1007/s00034-016-0455-8

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