Synthesis on a class of algebraic differentiators and application to nonlinear observation

Liu, Da‐Yan; Gibaru, Olivier; Perruquetti, Wilfrid

doi:10.1109/chicc.2014.6897044

Cited by 7 publications

(5 citation statements)

References 23 publications

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“…Riemann-Liouville derivatives of y can be given using a recursive way by (23) and the following formula:…”

Section: Theorem 2 Let Y Be a Signal Satisfying (1) Then Its Riemannmentioning

confidence: 99%

“…Successive differentiations: By successively taking differentiations to (23), the (l − β) th order Riemann-Liouville derivatives of y can be recursively given by:…”

Section: Theorem 2 Let Y Be a Signal Satisfying (1) Then Its Riemannmentioning

confidence: 99%

“…Error analysis for these errors can be given in a similar way as done for the algebraic integer order model-free differentiators (see [18,21,22,23] for more details). According to [18,21], if the value of τ is taken as the smallest root of P…”

Section: Tμκnnτ U(t I ) Contains Three Sources Of Errorsmentioning

confidence: 99%

“…6(a). By increasing the value of T , the noise error contribution in the estimation of u can be reduced, however the value of the time-delay will be increased (see [23] for more details). Finally, using the time-delayed input estimation, the obtained estimation of D 0.5 ti y(t i ) is shown in Fig.…”

Section: Example 2 Output Of a Linear Systemmentioning

confidence: 99%

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An algebraic fractional order differentiator for a class of signals satisfying a linear differential equation

et al. 2015

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This paper aims at designing a digital fractional order differentiator for a class of signals satisfying a linear differential equation to estimate fractional derivatives with an arbitrary order in noisy case, where the input can be unknown or known with noises. Firstly, an integer order differentiator for the input is constructed using a truncated Jacobi orthogonal series expansion. Then, a new algebraic formula for the Riemann-Liouville derivative is derived, which is enlightened by the algebraic parametric method. Secondly, a digital fractional order differentiator is proposed using a numerical integration method in discrete noisy case. Then, the noise error contribution is analyzed, where an error bound useful for the selection of the design parameter is provided. Finally, numerical examples illustrate the accuracy and the robustness of the proposed fractional order differentiator.

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“…Riemann-Liouville derivatives of y can be given using a recursive way by (23) and the following formula:…”

Section: Theorem 2 Let Y Be a Signal Satisfying (1) Then Its Riemannmentioning

confidence: 99%

“…Successive differentiations: By successively taking differentiations to (23), the (l − β) th order Riemann-Liouville derivatives of y can be recursively given by:…”

Section: Theorem 2 Let Y Be a Signal Satisfying (1) Then Its Riemannmentioning

confidence: 99%

Section: Tμκnnτ U(t I ) Contains Three Sources Of Errorsmentioning

confidence: 99%

Section: Example 2 Output Of a Linear Systemmentioning

confidence: 99%

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An algebraic fractional order differentiator for a class of signals satisfying a linear differential equation

et al. 2015

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“…Recall that the algebraic parametric method was introduced by Fliess and Sira-Ramírez for linear identification [26], and has been extended to many applications in noisy environment, such as design of integer order model-free differentiators (see, e.g. [27,28,29,30,31]) and parameter estimation (see, e.g. [32,33,34,35,36,37]).…”

Section: Introductionmentioning

confidence: 99%

Robust fractional order differentiators using generalized modulating functions method

Liu

Laleg‐Kirati

2015

Signal Processing

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This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.

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Survey on algebraic numerical differentiation: historical developments, parametrization, examples, and applications

Othmane

Kiltz

Rudolph

2022

International Journal of Systems Science

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Synthesis on a class of algebraic differentiators and application to nonlinear observation

Cited by 7 publications

References 23 publications

An algebraic fractional order differentiator for a class of signals satisfying a linear differential equation

An algebraic fractional order differentiator for a class of signals satisfying a linear differential equation

Robust fractional order differentiators using generalized modulating functions method

Survey on algebraic numerical differentiation: historical developments, parametrization, examples, and applications

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