We consider the stability and stabilization of impulsive stochastic delay differential equations ISDDEs . Using the Lyapunov-Razumikhin method, we obtain the sufficient conditions to guarantee the pth moment exponential stability of ISDDEs. Then the almost sure exponential stability is considered and the sufficient conditions of the almost sure exponential stability are obtained. Moreover, the ...

In this paper, a class of linear systems with multiple time delays is studied. The problem of exponential stability of time-delay systems has been investigated by using Lyapunov functional method. We will convert the system of multiple time delays into a single time delay system and show that if the old system is stable then the new one is so. Then we investigate the stability of converted new ...

This paper studies the problem of exponential stability analysis for recurrent neural networks with time-varying delay.By establishing a suitable augmented LyapunovCKrasovskii function and a novel sufficient condition is obtained to guarantee the exponential stability of the considered system.In order to get a less conservative results of the condition,zero equalities and reciprocally convex ap...

We analyze 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 H2-norm is not sufficient for the exponential stability with respect to the C1-norm. Hence, due to the nonlinearity, even in the case of classical solutions, the exponential stability depends strongly on the n...

This paper mainly deals with the almost surely exponential stability and exponential p-th moment stability for a class of stochastic Cohen–Grossberg neural networks with distributed delays and reaction–diffusion term. By constructing suitable Lyapunov functional, employing the nonnegative semi-martingale convergence theorem and applying matrix theory and stochastic analysis technique, two delay...

The problems of exponential stability and exponential convergence rate for a class of impulsive cellular neural networks with time-varying delays are studied. By means of the Lyapunov stability theory and discrete-time Halanay-type inequality technique, stability criteria for ensuring global exponential stability of noimpulsive discrete-time cellular neural networks and impulsive discrete-time ...

This paper discusses the well-posedness and exponential stability for nonlinear descriptor systems with discrete and distributed delays. The existence and uniqueness of the solution to the systems is first demonstrated by using the Picard’s method. In terms of the Lyapunov method, the exponential stability of the slow subsystems is obtained. From the existence and uniqueness of the solution, a ...

Over the last decades, various measures have been introduced to assess stability during walking. All of these measures assume that gait stability may be equated with exponential stability, where dynamic stability is quantified by a Floquet multiplier or Lyapunov exponent. These specific constructs of dynamic stability assume that the gait dynamics are time independent and without phase transiti...

Different methods for numerically stable computation of functions which are closely related to the exponential function are discussed. Such functions appear in the format of the most often used exponential integrators. A generalization of the method base on the tridiagonal reduction is proposed. The new approach, allows to compute all the functions included in the format of a general exponentia...