Pseudo-state feedback stabilization of commensurate fractional order systems

Farges, Christophe; Moze, Mathieu; Sabatier, Jocelyn

doi:10.1016/j.automatica.2010.06.038

Cited by 201 publications

(132 citation statements)

References 8 publications

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“…Note that the conditions given in Lemma 3.1 are equivalent to those given in Sabatier et al (2010b) and Farges et al (2010). Figure 1 shows the stable and unstable regions of the complex plane for 0 < α < 1.…”

Section: Stability Results For Fractional-order Dynamic Systemsmentioning

confidence: 97%

On the robustness of linear and non-linear fractional-order systems with non-linear uncertain parameters

Ndoye

Darouach

Voos

et al. 2015

IMA J Math Control Info

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This paper presents the robust stabilization problem of linear and non-linear fractional-order systems with non-linear uncertain parameters. The uncertainty in the model appears in the form of the combination of 'additive perturbation' and 'multiplicative perturbation'. Sufficient conditions for the robust asymptotical stabilization of linear fractional-order systems are presented in terms of linear matrix inequalities (LMIs) with the fractional-order 0 < α < 1. Sufficient conditions for the robust asymptotical stabilization of non-linear fractional-order systems are then derived using a generalization of the Gronwall-Bellman approach. Finally, a numerical example is given to illustrate the effectiveness of the proposed results.

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Section: Stability Results For Fractional-order Dynamic Systemsmentioning

confidence: 97%

On the robustness of linear and non-linear fractional-order systems with non-linear uncertain parameters

Ndoye

Darouach

Voos

et al. 2015

IMA J Math Control Info

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“…It is proved in [8] that the matrix (rX + rX) is real and invertible. So the linear matrix inequality (3.1) is also real.…”

Section: (T) Is Asymptotically Stable the Uncertain Fractional-ordermentioning

confidence: 99%

“…Moreover, there exist some uncertainties in the fractional-order control systems due to uncertain physical parameters, parametrical variations in time and so on. Recently, some stability analysis results for the fractional-order systems with interval uncertainties [1], [2], [5], [28], [36] or polytopic uncertainties [8], [9] have been presented. For example, the robust stability problem of fractional-order linear time-invariant(FO-LTI) interval systems described in the transfer function form was investigated in [36].…”

Section: Introductionmentioning

confidence: 99%

Robust stability bounds of uncertain fractional-order systems

Chen

et al. 2013

fcaa

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This paper considers the robust stability bound problem of uncertain fractional-order systems. The system considered is subject either to a twonorm bounded uncertainty or to a infinity-norm bounded uncertainty. The robust stability bounds on the uncertainties are derived. The fact that these bounds are not exceeded guarantees that the asymptotical stability of the uncertain fractional-order systems is preserved when the nominal fractionalorder systems are already asymptotically stable. Simulation examples are given to demonstrate the effectiveness of the proposed theoretical results.MSC 2010 : Primary 26A33; Secondary 34A08, 34D10, 93C73, 93D09, 93D21

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“…However, there are some existing possible Lyapunov-like functions in the literature [2,28,33]. On the other hand, some Lyapunovlike functions do not describe the state of the system, Mittag-Leffler stability for example, not the real state of the system [9,[26][27][28]. The Lyapunov-like function which are constructed from Mittag-Leffler stability are usually called fractional Lyapunov functions, and the techniques are referred to as the direct method of the fractional Lyapunov.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Mittag-Leffler stability of nonlinear fractional partial differential equations

Hanan¹,

Ahmad²,

Fadhel³

2017

J. Nonlinear Sci. Appl.

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This paper focuses on the application of fractional backstepping control scheme for nonlinear fractional partial differential equation (FPDE). Two types of fractional derivatives are considered in this paper, Caputo and the Grünwald-Letnikov fractional derivatives. Therefore, obtaining highly accurate approximations for this derivative is of a great importance. Here, the discretized approach for the space variable is used to transform the FPDE into a system of fractional differential equations. The convergence of the closed loop system is guaranteed in the sense of Mittag-Leffler stability. An illustrative example is given to demonstrate the effectiveness of the proposed control scheme.

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Pseudo-state feedback stabilization of commensurate fractional order systems

Cited by 201 publications

References 8 publications

On the robustness of linear and non-linear fractional-order systems with non-linear uncertain parameters

On the robustness of linear and non-linear fractional-order systems with non-linear uncertain parameters

Robust stability bounds of uncertain fractional-order systems

Nonlinear Mittag-Leffler stability of nonlinear fractional partial differential equations

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