In this paper, we shall present sufficient conditions for the ψ-exponential stability of a class of nonlinear impulsive differential equations. We use the Lyapunov method with functions that are not necessarily differentiable. In the last section, we give some examples to support our theoretical results. Keywords—Exponential stability, globally exponential stability, impulsive differential equa...

Global exponential stability is a desirable property for dynamic systems. This paper studies the global exponential stability of several existing recurrent neural networks for solving linear programming problems, convex programming problems with interval constraints, convex programming problems with nonlinear constraints, and monotone variational inequalities. In contrast to the existing result...

The main purpose of this paper is to establish some new results onthe superstability and stability via a fixed point approach forthe Pexiderized exponential equation, i.e.,$$|f(x+y)-g(x)h(y)|leq psi(x,y),$$where $f$, $g$ and $h$ are three functions from an arbitrarycommutative semigroup $S$ to an arbitrary unitary complex Banachalgebra and also $psi: S^{2}rightarrow [0,infty)$ is afunction. Fur...

This paper investigates the pth moment globally uniformly exponential stability of a class of impulsive stabilization of stochastic delay differential equations,and the pth moment exponential stability criteria is established by using theLyapunov–Razumikhin method. Keywords—Stochastic delay differential equations; Exponential stability ; Lyapunov-Razumikhin method ; Impulsive control

The aim of this paper is to establish necessary and sufficient conditions for exponential stability of semigroups of linear operators and to show how this conditions can be applied in order to characterize the exponential dichotomy. First, we prove that an exponentially bounded semigroup is exponentially stable if and only if it is (l(N, X), l∞(N, X))-stable, where p ∈ (1,∞). After that this re...

In correcting a small mistake in [10], we can prove a new result on non-exponential stability for a coupled system arising in resonators. This also gives another (surprising and) simple example for a thermoelastic system changing from exponential stability to non-exponential stability when changing from Fourier’s law to Cattaneo’s law in the modeling of heat conduction.

In this paper, we discuss delayed periodic dynamical systems, compare capability of criteria of global exponential stability in terms of various L (1 ≤ p < ∞) norms. A general approach to investigate global exponential stability in terms of various L (1 ≤ p < ∞) norms is given. Sufficient conditions ensuring global exponential stability are given, too. Comparisons of various stability criteria ...

Estimate of exponential convergence rate and exponential stability are studied for a class of neural networks which includes the Hopfield neural networks and the cellular neural networks. Both local and global exponential convergence is discussed. Theorems for estimate of exponential convergence rate are established and the bounds on the rate of convergence are given. The domains of attraction ...

Abstract. We analyse dissipative boundary conditions for nonlinear hyperbolic systems in one space dimension. We show that a known sufficient condition for exponential stability with respect to the H-norm is not sufficient for the exponential stability with respect to the C-norm. Hence, due to the nonlinearity, even in the case of classical solutions, the exponential stability depends strongly ...