On the finite-time boundary dissipative for a class of hyperbolic systems. The networks example

Belgacem, Ghada Ben; Jammazi, Chaker

doi:10.1016/j.ifacol.2016.07.435

Cited by 2 publications

(2 citation statements)

References 28 publications

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“…Remark It is well known that the ODE

\overset{w}{true} = - s g n false(w false) false| w {false|}^{β}

, with

w \in ℝ

and β ∈ (0, 1), is finite‐time stable (see e.g 29 τ=false|wfalse(0false)false|1−β1−β.…”

Section: Resultsmentioning

confidence: 99%

Some results on the internal finite‐time stabilization of vibrating strings with interior mass

Belgacem

Jammazi

2020

Math Methods in App Sciences

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In this paper, the problem of internal finite-time stabilization for 1-D coupled wave equations with interior point mass is handled. The nonlinear stabilizing feedback law leads, in closed-loop, to nonlinear evolution equations where Kato theory is used to prove the well-posedness. In addition, it is showed that in some cases, the solution of this hybrid system is constant in finite-time if we use Neumann boundary conditions. This result can be improved (in complete finite-time stability sense) if we change the above feedback.

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“…Remark It is well known that the ODE

\overset{w}{true} = - s g n false(w false) false| w {false|}^{β}

, with

w \in ℝ

and β ∈ (0, 1), is finite‐time stable (see e.g 29 τ=false|wfalse(0false)false|1−β1−β.…”

Section: Resultsmentioning

confidence: 99%

Some results on the internal finite‐time stabilization of vibrating strings with interior mass

Belgacem

Jammazi

2020

Math Methods in App Sciences

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“…In addition, the finite-time stabilization of Kinematic waves that exhibit time switching between boundary conditions is proved in [4] and illustrated through the examples of SMB chromatography and the Ramp-metering control for road traffic network.…”

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confidence: 99%

On the finite-time Bhat-Bernstein feedbacks for the strings connected by point mass

Belgacem¹,

Jammazi²

2019

Discrete &Amp; Continuous Dynamical Systems - B

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In this article, the problem of finite-time stabilization of two strings connected by point mass is discussed. We use the so-called Riemann coordinates to convert the study system into four transport equations coupled with the dynamic of the charge. We act by Bhat-Bernstein feedbacks in various positions (two extremities, the point mass and one of boundaries, only on the point mass,...) and we show that in some cases the nature of the stability depends sensitively on the physical parameters of the system.

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On the finite-time boundary dissipative for a class of hyperbolic systems. The networks example

Cited by 2 publications

References 28 publications

Some results on the internal finite‐time stabilization of vibrating strings with interior mass

Some results on the internal finite‐time stabilization of vibrating strings with interior mass

On the finite-time Bhat-Bernstein feedbacks for the strings connected by point mass

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