Uniform Exponential Stability ofApproximations in Linear Viscoelasticity
نویسندگان
چکیده
In this paper, we rst study the abstract setting of linear vis-coelasticity and under reasonable conditions on the kernel we prove the exponential stability of the associated semigroup. Secondly, we study the general approximate schemes proposed by Banks and Burns, by Ito and Kappel, and by Fabiano and Ito, respectively. The uniformly exponential stability of semigroups associated with these approximate schemes is proved.
منابع مشابه
Construction of strict Lyapunov function for nonlinear parameterised perturbed systems
In this paper, global uniform exponential stability of perturbed dynamical systems is studied by using Lyapunov techniques. The system presents a perturbation term which is bounded by an integrable function with the assumption that the nominal system is globally uniformly exponentially stable. Some examples in dimensional two are given to illustrate the applicability of the main results.
متن کاملUniform Stabilization of n-Dimensional Vibrating Equation Modeling ‘Standard Linear Model’ of Viscoelasticity
In this paper, we deal with the elastic vibrations of flexible structures modeled by the ‘standard linear model’ of viscoelasticity in n-dimensional space. We study the uniform exponential stabilization of such kind of vibrations after incorporating separately very small amount of passive viscous damping and internal material damping of Kelvin-Viogt type in the model. Explicit forms of exponent...
متن کاملExponential Stability and Exponential Instability for Linear Skew-product Flows
We give characterizations for uniform exponential stability and uniform exponential instability of linear skew-product flows in terms of Banach sequence spaces and Banach function spaces, respectively. We present a unified approach for uniform exponential stability and uniform exponential instability of linear skew-product flows, extending some stability theorems due to Neerven, Datko, Zabczyk ...
متن کاملUniform exponential stability for linear discrete time systems with stochastic perturbations in Hilbert spaces
In this paper we study the exponential and uniform exponential stability problem for linear discrete time-varying systems with independent stochastic perturbations. We give two representations of the solutions of the discussed systems and we use them to obtain necessary and sufficient conditions for the two types of stability. A deterministic characterization of the uniform exponential stabilit...
متن کاملExponential Stability of Linear Time-Invariant Systems on Time Scales
Several notions of exponential stability of linear time-invariant systems on arbitrary time scales are discussed. We establish a necessary and sufficient condition for the existence of uniform exponential stability. Moreover, we characterize the uniform exponential stability of a system by the spectrum of its matrix. In general, exponential stability of a system can not be characterized by the ...
متن کامل