A comment on “Exponential stability of nonlinear delay equation with constant decay rate via perturbed system method”

Makhlouf, Abdellatif Ben; Hammami, Mohamed

doi:10.1007/s12555-014-0015-6

Cited by 11 publications

(3 citation statements)

References 10 publications

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“…Proof. In this proof, we will demonstrate the uniformly exponential convergence (Ben Makhlouf and Hammami, 2014, 2015) of the pair ( e y , f ^ s ) to the set χ . Let us define the augmented error as e ¯ = z − z ^ .…”

Section: Integral Observer With Sliding-mode Termsmentioning

confidence: 96%

Robust integral-observer-based fault estimation for Lipschitz nonlinear systems with time-varying uncertainties

Zemzemi

Kamel

Toumi

et al. 2018

Transactions of the Institute of Measurement and Control

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This paper addresses the problem of state estimation and sensor fault reconstruction conjointly for a class of nonlinear systems with time-varying uncertainties for which the nonlinear characteristic satisfies the Lipschitz circumstance. A hybrid approach based on an integral observer and sliding-mode theory has been proposed in order to model sensor fault as a virtual actuator one. For the augmented model, the observer matching condition is not satisfied. To overcome this problem, a new method, which improves the design approach and enhances the rapidity of the fault estimation convergence, has been proposed. The fault estimation error effect is minimized by integrating the H ∞ disturbance attenuation level. The proposed design is formulated and derived as a linear matrix inequality problem. Parameters of this observer are calculated through the linear matrix inequality technique. The proposed method has been validated through an example of a single-link manipulator robot. Simulation results show that this approach can estimate the state and the sensor fault successfully, despite the time-varying uncertainties and the presence of unknown inputs.

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Section: Integral Observer With Sliding-mode Termsmentioning

confidence: 96%

Robust integral-observer-based fault estimation for Lipschitz nonlinear systems with time-varying uncertainties

Zemzemi

Kamel

Toumi

et al. 2018

Transactions of the Institute of Measurement and Control

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“…The second is the time delay that is introduced as a result of image acquisition, image processing and visual information transmission (Gortcheva et al, 2001; Jean and Lian, 2012; Wang et al, 2012). It is well known that the foremost source of instability and system performance degradation is time delay (Huong and Trinh, 2016; Huong, 2016; Makhlouf and Hammami, 2014; Wang et al, 2014b; Xie and Chen, 2013; Zhang et al, 2015a).…”

Section: Introductionmentioning

confidence: 99%

State observer for linear system with unknown input disturbance and sampled and delayed output with measurement noise

Mohammed

Wang²,

Tian

2018

Transactions of the Institute of Measurement and Control

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This paper addresses the sampled and unknown time-varying delayed output problem of the continuous-time linear system with unknown input disturbance and measurement noise. Based on the piecewise continuous hybrid system and extended functional observer, a robust hybrid extended observer is proposed to estimate the non-delayed continuous state from the sampled and delayed measurements when the time delay is unknown time-varying. The advantages of the designed observer are the quite simple structure, robustness to dealing with measurement noise, and ability to estimate the system state with accuracy under the influence of unknown input disturbance. Furthermore, the proposed observer is able to estimate the non-delayed continuous state and unknown input disturbance, in particular for the issue of fault estimation and perturbation disturbance simultaneously. The stability of the robust hybrid extended observer is illustrated and analyzed. Moreover, to show the effectiveness of the proposed observer, a comparison with the delayed Luenberger observer is performed via a numerical example. Finally, the simulation results are demonstrated.

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“…The stability analysis of nonlinear systems under time delays is usually more difficult compared with systems without time delays [7,13,22]. Time delay is a property of many dynamical systems such as, communications, embedded systems, mechanical, tele-operation, biological, electrical, and many other applications [8,20,29].…”

Section: Introductionmentioning

confidence: 99%

State feedback control law for a class of nonlinear time-varying system under unknown time-varying delay

et al. 2015

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In this paper, the problem of stabilization of a specific class of nonlinear dynamical system with unknown, bounded, time-varying delay is considered. A new stabilizing control law guarantees the practical stability of the system. A modified extended control law leads to the exponential stability. A Lyapunov function is chosen, and sufficient assumptions are provided in order to prove the stability of the proposed feedback system. Simulation results are addressed to show the effectiveness of the suggested control design method.

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A comment on “Exponential stability of nonlinear delay equation with constant decay rate via perturbed system method”

Abstract: In this paper, we point out that inequality (7) of [5] is not correct. A feasible modified and corrected version of the main result is presented. Furthermore, some numerical examples are given to illustrate the applicability of the modified result.

Cited by 11 publications

References 10 publications

Robust integral-observer-based fault estimation for Lipschitz nonlinear systems with time-varying uncertainties

Robust integral-observer-based fault estimation for Lipschitz nonlinear systems with time-varying uncertainties

State observer for linear system with unknown input disturbance and sampled and delayed output with measurement noise

State feedback control law for a class of nonlinear time-varying system under unknown time-varying delay

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