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Novel frequency-domain criterion for elimination of limit cycles in a class of digital filters with single saturation nonlinearity

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  • Singh, Vimal

Abstract

A frequency-domain criterion for the elimination of limit cycles in a class of digital filters utilizing single saturation nonlinearity is presented. The criterion is derived by exploiting the structural properties of the system under consideration in a greater detail. A novel feature of the criterion is that it takes the form of a matrix inequality, despite the fact that there is single nonlinearity in the system. An example showing the effectiveness of the criterion is given.

Suggested Citation

  • Singh, Vimal, 2008. "Novel frequency-domain criterion for elimination of limit cycles in a class of digital filters with single saturation nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 178-183.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:1:p:178-183
    DOI: 10.1016/j.chaos.2006.10.059
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    References listed on IDEAS

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    1. He, Ji-Huan, 2005. "Limit cycle and bifurcation of nonlinear problems," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 827-833.
    2. Ye, Zhiyong & Han, Maoan, 2006. "Singular limit cycle bifurcations to closed orbits and invariant tori," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 758-767.
    3. Singh, Vimal, 2008. "Suppression of limit cycles in second-order companion form digital filters with saturation arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 677-681.
    4. Adimy, Mostafa & Crauste, Fabien & Halanay, Andrei & Neamţu, Mihaela & Opriş, Dumitru, 2006. "Stability of limit cycles in a pluripotent stem cell dynamics model," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1091-1107.
    5. Singh, Vimal, 2007. "A new frequency-domain criterion for elimination of limit cycles in fixed-point state-space digital filters using saturation arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 813-816.
    6. Yu, P. & Han, M., 2005. "Small limit cycles bifurcating from fine focus points in cubic order Z2-equivariant vector fields," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 329-348.
    7. Ramos, J.I., 2006. "Piecewise-linearized methods for oscillators with limit cycles," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1229-1238.
    8. Wang, S. & Yu, P., 2005. "Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1317-1335.
    9. Wu, Yuhai & Han, Maoan & Liu, Xuanliang, 2005. "On the study of limit cycles of a cubic polynomials system under Z4-equivariant quintic perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 999-1012.
    10. Singh, Vimal, 2007. "Modified LMI condition for the realization of limit cycle-free digital filters using saturation arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1448-1453.
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