摘要 :
In a recent paper, Rodrigues and Sola-Morales construct an example of a continuously Frechet differentiable discrete dynamical system in a separable Hilbert space for which the origin is an exponentially asymptotically stable fixe...
展开
In a recent paper, Rodrigues and Sola-Morales construct an example of a continuously Frechet differentiable discrete dynamical system in a separable Hilbert space for which the origin is an exponentially asymptotically stable fixed point, although its derivative at 0 has spectral radius greater than one. For maps on general Banach spaces we demonstrate that the slightly stronger, but also widely used concept of exponential stability allows a complete characterization in terms of the spectral radius. Moreover, under a spectral gap condition valid for compact and finite-dimensional linearizations these two stability notions are shown to be equivalent. (C) 2020 The Author(s). Published by Elsevier Inc.
收起
摘要 :
The aim of this paper is to give some characterizations for weak exponential stability properties of evolution operators in Banach spaces. Variants for weak exponential stability of some well-known results in uniform stability the...
展开
The aim of this paper is to give some characterizations for weak exponential stability properties of evolution operators in Banach spaces. Variants for weak exponential stability of some well-known results in uniform stability theory (Bue and Niculescu (2009) [1], Daleckij and Krein (1974) [2], Datko (1973) [3], Rolewicz (1986) [7], Stoica and Megan (2009) [8]) are obtained.
收起
摘要 :
A reason for applying the direct method of Lyapunov to artificial neural networks (ANNs) is to design dynamical neural networks so that they exhibit global asymptotic stability. Lyapunov functions that frequently appear in the ANN...
展开
A reason for applying the direct method of Lyapunov to artificial neural networks (ANNs) is to design dynamical neural networks so that they exhibit global asymptotic stability. Lyapunov functions that frequently appear in the ANN literature include the quadratic function, the Persidskii function, and the Lure-Postnikov function. This contribution revisits the quadratic function and shows that via Krasovskii-like stability criteria, it is possible to have a very simple and systematic procedure to obtain not only new and generalized results but also well-known sufficient conditions for convergence established recently by non-Lyapunov methods, such as the matrix measure and nonlinear measure.
收起
摘要 :
This paper investigates the system proposed by a wave equation and a heat equation of type III in one part of the domain; a wave equation and a heat equation of type II in another part of the domain, coupled in a certain pattern. ...
展开
This paper investigates the system proposed by a wave equation and a heat equation of type III in one part of the domain; a wave equation and a heat equation of type II in another part of the domain, coupled in a certain pattern. In this paper we prove the exponential stability of the solutions under suitable conditions for the thermal conductivity and coupling term. (C) 2018 Elsevier Inc. All rights reserved.
收起
摘要 :
In this work, we study the effect of the positions of the dissipative mechanisms on a bar of three components; two of them formed by viscous materials of Kelvin Voight type. The difference is that in one of the viscous components ...
展开
In this work, we study the effect of the positions of the dissipative mechanisms on a bar of three components; two of them formed by viscous materials of Kelvin Voight type. The difference is that in one of the viscous components the constitutive law is discontinuous, while in the other is differentiable. The third component is purely elastic, without any dissipative mechanism. We show that the system is exponentially stable if and only if the viscous component, with discontinuous constitutive law, is not in the center of the bar. In other case, we show the lack of exponential stability, and that the solutions still decay but now polynomially to zero.
收起
摘要 :
In this paper, we are concerned with the asymptotic behavior of the eigenvalues arising from a one-dimensional linear thermoelastic system with the Dirichlet-Dirichlet boundary condition. It is shown that the eigenfrequency asympt...
展开
In this paper, we are concerned with the asymptotic behavior of the eigenvalues arising from a one-dimensional linear thermoelastic system with the Dirichlet-Dirichlet boundary condition. It is shown that the eigenfrequency asymptotically falls on two branches: one branch is along the negative horizontal axis in the complex plane and the other branch is asymptotic to the vertical line Re lambda = -gamma(2)/2k. These results lead to the exponential stability of the system and also provide a proof for the numerical simulation results by Liu and Zheng (1993, Quart. Appl. Math., 51, 535-545). (C) 1997 Academic Press. [References: 6]
收起
摘要 :
This paper investigates the stability for a delayed recurrent neural network. Sufficient conditions are obtained for ascertaining the global asymptotic stability of the unique equilibrium of the network based on LMI technique. The...
展开
This paper investigates the stability for a delayed recurrent neural network. Sufficient conditions are obtained for ascertaining the global asymptotic stability of the unique equilibrium of the network based on LMI technique. The results are computationally efficient, since they are in the form of linear matrix inequality (LMI), which can be checked easily by various recently developed convex optimization algorithms. Besides, the analysis approach allows one to consider different types of activation functions, such as piecewise linear, sigmoids with bounded activations as well as Clsmooth sigmoids. In the end of this paper two illustrative examples are also provided to show the effectiveness of our results. (c) 2005 Elsevier Ltd. All rights reserved.
收起
摘要 :
The paper considers some concepts of nonuniform asymptotic stability for skew-evolution semiflows in Banach spaces, which we have introduced in [Megan, M. and Stoica, C., Exponential instability of skewevolution semiflows in Banac...
展开
The paper considers some concepts of nonuniform asymptotic stability for skew-evolution semiflows in Banach spaces, which we have introduced in [Megan, M. and Stoica, C., Exponential instability of skewevolution semiflows in Banach spaces, Stud. Univ. Babes-Bolyai Math., LIII (2008), No. 1,17-24] and for which we present equivalent definitions, as well as integral characterizations in a nonuniform setting. Some examples are included to illustrate the results and to clarify the differences between the uniform and nonuniform cases.
收起
摘要 :
We study the well-posedness and decay properties of a one-dimensional thermoelastic laminated beam system either with or without structural damping, of which the heat conduction is given by Fourier's law effective in the rotation ...
展开
We study the well-posedness and decay properties of a one-dimensional thermoelastic laminated beam system either with or without structural damping, of which the heat conduction is given by Fourier's law effective in the rotation angle displacements. We show that the system is well-posed by using the Lumer-Philips theorem, and prove that the system is exponentially stable if and only if the wave speeds are equal, by using the perturbed energy method and Gearhart-Herbst-Pruss-Huang theorem. Furthermore, we show that the system with structural damping is polynomially stable provided that the wave speeds are not equal, by using the second-order energy method. When the speeds are not equal, whether the system without structural damping may has polynomial stability is left as an open problem.
收起
原文获取