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标题:Proper discretization of homogeneous differentiators
时间:2020-02-14 17:59:43
DOI:10.1016/j.automatica.2014.05.028
作者:Livne, Miki; Levant, Arie
关键词:Sliding mode control; Observation; Finite-time stability
出版源: 《Automatica》 ,50 (8) :2007-2014
摘要:Homogeneous sliding-mode-based differentiators (HD) are known to provide for the high-accuracy robust estimation of derivatives in the presence of sampling noises and discrete measurements, provided that the differentiator dynamics evolve in continuous time. The popular one-step Euler discrete-time implementation is proved to cause differentiation accuracy deterioration, if the differentiation order exceeds 1. A novel discrete-time realization of the HD is proposed, which preserves the ultimate accuracy of the continuous-time HD also with discrete measurements.
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目录:
  • Proper discretization of homogeneous differentiators
    • Introduction
    • Preliminaries: HOSM-based differentiation and discretization problem
    • Accuracy of one-step Euler differentiator discretization
      • Asymptotic accuracy in the case of variable sampling intervals
      • Asymptotic accuracy in the case of constant sampling intervals
    • Proper discretization of homogeneous SM-based differentiators
    • Asymptotic accuracy of disturbed homogeneous inclusions
    • Simulation results
      • One-step Euler approximation
      • Homogeneous discrete-time differentiator (HDD)
    • Conclusions
    • Proof of Theorem 1
    • Proof of Theorem 2
    • Proof of Theorem 3
    • Proof of Lemma 1
    • References

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