scholarly journals Boundary stabilization for a star-shaped network of variable coefficients strings linked by a point mass

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Walid Boughamda
Keyword(s):  
Closed Loop ◽  
Asymptotic Expression ◽  
Variable Coefficients ◽  
Point Mass ◽  
Closed Loop System ◽  
Optimal Decay ◽  
Optimal Decay Rate ◽  
Generalized Eigenfunctions ◽  
The Common ◽  
Stability Results

<p style='text-indent:20px;'>This study is concerned with the pointwise stabilization for a star-shaped network of <inline-formula><tex-math id="M1">\begin{document}$ N $\end{document}</tex-math></inline-formula> variable coefficients strings connected at the common node by a point mass and subject to boundary feedback dampings at all extreme nodes. It is shown that the closed-loop system has a sequence of generalized eigenfunctions which forms a Riesz basis for the state Hilbert space. As a consequence, the spectrum-determined growth condition fulfills. In the meanwhile, the asymptotic expression of the spectrum is presented, and the exponential stability of the system is obtained by giving the optimal decay rate. We prove also that a phenomenon of lack of uniform stability occurs in the absence of damper at one extreme node. This paper reconfirmed the main stability results given by Hansen and Zuazua [SIAM J. Control Optim., <b>33</b> (1995), 1357-1391] in a very particular case.</p>

scholarly journals Stabilization of Variable Coefficients Euler-Bernoulli Beam with Viscous Damping under a Force Control in Rotation and Velocity Rotation

2017 ◽  
Vol 9 (6) ◽  
pp. 1
Author(s):  
Bomisso G. Jean Marc ◽  
Tour\'{e} K. Augustin ◽  
Yoro Gozo
Keyword(s):  
Exponential Stability ◽  
Force Control ◽  
Riesz Basis ◽  
Closed Loop ◽  
Variable Coefficients ◽  
Viscous Damping ◽  
Closed Loop System ◽  
Bernoulli Beam ◽  
Spectral System ◽  
Euler Bernoulli Beam

This paper investigates the problem of exponential stability for a damped Euler-Bernoulli beam with variable coefficients clamped at one end and subjected to a force control in rotation and velocity rotation. We adopt the Riesz basis approach for show that the closed-loop system is a Riesz spectral system. Therefore, the exponential stability and the spectrum-determined growth condition are obtained.

scholarly journals Synchronization of the Extended Bonhoffer-Van der Pol Oscillators

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Mohamed Zribi ◽  
Saleh Alshamali
Keyword(s):  
Closed Loop ◽  
Sliding Mode ◽  
Lyapunov Theory ◽  
Closed Loop System ◽  
Van Der Pol ◽  
Parameter Perturbations ◽  
Van Der Pol Oscillators ◽  
Response Systems ◽  
Single Input ◽  
Stability Results

This paper deals with the synchronization of two extended Bonhoffer-Van der Pol (B-VDP) oscillators. A Lyapunov-based controller and a sliding mode controller are proposed for the synchronization of the oscillators. Both design schemes use a single input controller acting on one state only. Asymptotic stability results for the closed-loop system are derived using Lyapunov theory. It is shown that the proposed controllers effectively synchronize the driver and the response systems for the case when nominal values of the system parameters are used, and for the case when parameter perturbations are introduced. Simulation results are presented to show the effectiveness of the proposed controllers.

scholarly journals Stability results of some first order viscous hyperbolic systems

2019 ◽  
Vol 25 ◽  
pp. 33
Author(s):  
Serge Nicaise
Keyword(s):  
Spectral Analysis ◽  
Decay Rate ◽  
Exponential Decay ◽  
Hyperbolic Systems ◽  
Natural Assumption ◽  
Abstract Problem ◽  
First Order ◽  
Optimal Decay ◽  
Optimal Decay Rate ◽  
Stability Results

In this paper, we first introduce an abstract viscous hyperbolic problem for which we prove exponential decay under appropriated assumptions. We then give some illustrative examples, like the linearized viscous Saint-Venant system. In order to achieve the optimal decay rate, we also perform a detailed spectral analysis of our abstract problem under a natural assumption satisfied by various examples. We finally consider the boundary stabilizability of the linearized viscous Saint-Venant system on trees.

scholarly journals Stabilization of the Wave Equation with Boundary Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hao Li ◽  
Changsong Lin ◽  
Shupeng Wang ◽  
Yanmei Zhang
Keyword(s):  
Wave Equation ◽  
Closed Loop ◽  
Nonlinear Boundary ◽  
Variable Coefficients ◽  
Time Varying ◽  
Closed Loop System ◽  
Weakly Nonlinear ◽  
Delay Term ◽  
Time Varying Delay ◽  
Varying Delay

We study the stabilization of the wave equation with variable coefficients in a bounded domain and a time-varying delay term in the time-varying, weakly nonlinear boundary feedbacks. By the Riemannian geometry methods and a suitable assumption of nonlinearity, we obtain the uniform decay of the energy of the closed loop system.

Safety and Performance of the Omnipod®Hybrid Closed-Loop System in Adolescents with Type 1 Diabetes over Five Days Under Free-Living Conditions

Diabetes ◽  
2018 ◽  
Vol 67 (Supplement 1) ◽  
pp. 1376-P
Author(s):  
GREGORY P. FORLENZA ◽  
BRUCE BUCKINGHAM ◽  
JENNIFER SHERR ◽  
THOMAS A. PEYSER ◽  
JOON BOK LEE ◽  
...  
Keyword(s):  
Type 1 Diabetes ◽  
Closed Loop ◽  
Living Conditions ◽  
Loop System ◽  
Closed Loop System ◽  
Free Living ◽  
And Performance ◽  
Free Living Conditions

1066-P: Improvement in Time-in-Range (TIR) with Real-Life Use of Hybrid Closed-Loop System in Patients with Type 1 Diabetes (T1D)

Diabetes ◽  
2019 ◽  
Vol 68 (Supplement 1) ◽  
pp. 1066-P
Author(s):  
HALIS K. AKTURK ◽  
DOMINIQUE A. GIORDANO ◽  
HAL JOSEPH ◽  
SATISH K. GARG ◽  
JANET K. SNELL-BERGEON
Keyword(s):  
Type 1 Diabetes ◽  
Closed Loop ◽  
Real Life ◽  
Loop System ◽  
Closed Loop System ◽  
Time In Range

Safety and Performance of the Omnipod® Hybrid Closed-Loop System in Adults with Type 1 Diabetes over Five Days Under Free-Living Conditions

Diabetes ◽  
2018 ◽  
Vol 67 (Supplement 1) ◽  
pp. 207-OR
Author(s):  
BRUCE A. BUCKINGHAM ◽  
JENNIFER SHERR ◽  
GREGORY P. FORLENZA ◽  
THOMAS A. PEYSER ◽  
JOON BOK LEE ◽  
...  
Keyword(s):  
Type 1 Diabetes ◽  
Closed Loop ◽  
Living Conditions ◽  
Loop System ◽  
Closed Loop System ◽  
Free Living ◽  
And Performance ◽  
Free Living Conditions
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