Exponential stabilization of 1-d wave equation with input delay
نویسندگان
چکیده
Abstract: In this paper, we consider the stabilization problem of 1-d wave equation with input delay. Suppose that the wave system is fixed at one end whereas a control force is applied at other end. Here we consider the control force of the form αu(t) + βu(t − τ) where τ is the time delay. In this paper we find a feedback control law that stabilizes exponentially the system for any |α| ̸= |β| and τ > 0.
منابع مشابه
Stabilization of a Type III Thermoelastic Bresse System with Distributed Delay-time
In this paper, we investigate a Bresse-type system of thermoelasticity of type III in the presence of a distributed delay. We prove the well-posedness of the problem. Furthermore, an exponential stability result will be shown without the usual assumption on the wave speeds. To achieve our goals, we make use of the semigroup method and the energy method.
متن کاملNew Approach to Exponential Stability Analysis and Stabilization for Delayed T-S Fuzzy Markovian Jump Systems
This paper is concerned with delay-dependent exponential stability analysis and stabilization for continuous-time T-S fuzzy Markovian jump systems with mode-dependent time-varying delay. By constructing a novel Lyapunov-Krasovskii functional and utilizing some advanced techniques, less conservative conditions are presented to guarantee the closed-loop system is mean-square exponentially stable....
متن کاملExponential Stabilization of 1-d Wave Equation with Distributed Disturbance
In this paper, we consider the stabilization problem of a one-dimensional wave equation with unknown disturbance. In order to stabilize the system with disturbance, we design a distributed feedback controller by employing the idea of sliding mode control technology. For the resulted nonlinear closed-loop system, we prove its solvability by using the maximal monotone operator. Further we prove t...
متن کاملStabilization of the wave equation with a delay term in the boundary or internal feedbacks
In this paper we consider, in a bounded and smooth domain, the wave equation with a delay term in the boundary condition. We also consider the wave equation with a delayed velocity term and mixed Dirichlet-Neumann boundary condition. In both cases, under suitable assumptions, we prove exponential stability of the solution. These results are obtained by introducing suitable energies and by using...
متن کاملInterior feedback stabilization of wave equations with time dependent delay
We study the stabilization problem by interior (weak/strong) damping of the wave equation with boundary or internal time–varying delay feedback in a bounded and smooth domain Ω ⊂ IR. By introducing suitable Lyapunov functionals exponential stability estimates are obtained if the delay effect is appropriately compensated by the internal damping. 2000 Mathematics Subject Classification: 35L05, 93D15
متن کامل