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.

scholarly journals Robust H∞ Observer-Based Control Design for Discrete-Time Nonlinear Systems With Time-Varying Delay

2021 ◽  
Vol 20 ◽  
pp. 88-97
Author(s):  
Mengying Ding ◽  
Yali Dong
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the problem of robust H∞ observer-based control for a class of discrete-time nonlinear systems with time-varying delays and parameters uncertainties. We propose an observer-based controller. By constructing an appropriate Lyapunov-Krasovskii functional, some sufficient conditions are developed to ensure the closed-loop system is robust asymptotically stable with H∞ performance in terms of the linear matrix inequalities. Finally, a numerical example is given to illustrate the efficiency of proposed methods.

scholarly journals Global existence and energy decay of solutions for a wave equation with a time-varying delay term

Mathematica ◽  
2021 ◽  
Vol 63 (86) (1) ◽  
pp. 32-46
Author(s):  
Benguessoum Aissa
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Existence Of Solutions ◽  
Time Varying ◽  
Rate Estimate ◽  
Delay Term ◽  
Time Varying Delay ◽  
Global Existence Of Solutions ◽  
Decay Of Solutions ◽  
Varying Delay

We consider, in a bounded domain, a certain wave equation with a weak internal time-varying delay term. Under appropriate conditions, we prove global existence of solutions by the Faedo-Galerkin method and establish a decay rate estimate for the energy using the multiplier method.

scholarly journals Uniform decay for a viscoelastic wave equation with density and time-varying delay in Rn

Filomat ◽  
2019 ◽  
Vol 33 (3) ◽  
pp. 961-970
Author(s):  
Salah Zitouni ◽  
Khaled Zennir ◽  
Lamine Bouzettouta
Keyword(s):  
Wave Equation ◽  
Relaxation Function ◽  
Time Varying ◽  
Delay Term ◽  
Time Varying Delay ◽  
Viscoelastic Wave Equation ◽  
Viscoelastic Wave ◽  
Linear Viscoelastic ◽  
Energy Perturbation ◽  
Varying Delay

A linear viscoelastic wave equation with density and a time-varying delay term in the internal feedback is considered. Under suitable assumptions on the relaxation function, we establish a decay result of solution for by using energy perturbation method in the space Rn (n > 2). We extend a recent result in Feng [10].

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