This paper considers the stability of both continuous and discrete time-varying linear systems. Stability estimates are obtained in either case in terms of the Lipschitz constant for the governing matrices and the assumed uniform decay rate of the corresponding frozen time linear systems. The main techniques used in the analysis are comparison methods, scaling and the application of continuous ...

We prove that a general system of variational difference equations is uniformly exponentially stable if and only if certain associated sets are of the second category. We also deduce necessary and sufficient conditions for uniform exponential stability of systems with uniformly bounded coefficients. We apply our results for the study of exponential stability of linear skew-product flows, genera...

Relatively little is known about the ability of numerical methods for stochastic differential equations (SDEs) to reproduce almost sure and small-moment stability. Here, we focus on these stability properties in the limit as the timestep tends to zero. Our analysis is motivated by an example of an exponentially almost surely stable nonlinear SDE for which the Euler–Maruyama (EM) method fails to...

In this Letter, the globally exponential stability for a class of neural networks including Hopfield neural networks and cellular neural networks with time-varying delays is investigated. Based on the Lyapunov stability method, a novel and less conservative exponential stability condition is derived. The condition is delay-dependent and easily applied only by checking the Hamiltonian matrix wit...

This paper considers 2D feedback systems modeled a by repetitive process where both the forward path and the feedback paths are nonlinear. Using a Lyapunov function approach, sufficient conditions for exponential stability are obtained and in the linear case the connection between exponential stability and the existing stability along the pass theory is established. The results are then extende...

The global exponential stability is investigated for neural networks with interval time-varying delays. Based on the Leibniz-Newton formula and linear matrix inequality technique, delay-dependent stability criteria are proposed to guarantee the exponential stability of neural networks with interval time-varying delays. Some numerical examples and comparisons are provided to show that the propos...

This paper considers the global robust exponential stability of time-varying delayed neural networks with discontinuous activation functions and norm-bounded uncertainties. Based on the Lyapunov– Krasovskii stability theory, we originally analyze the global robust exponential stability of discontinuous neural networks with time-varying delays in view of the linear matrix inequalities given to v...

We are concerned with the exponential mean-square stability of two-step Maruyama methods for stochastic differential equations with time delay. We propose a family of schemes and prove that it can maintain the exponential mean-square stability of the linear stochastic delay differential equation for every step size of integral fraction of the delay in the equation. Numerical results for linear ...

We address the stability property of the FAST TCP congestion control algorithm. Based on a continuous-time dynamic model of the FAST TCP network, we establish that FAST TCP in itself is globally exponentially stable without any specific conditions on the congestion control parameter or the update gain. Simulation results demonstrate the validity of the global exponential stability of FAST TCP. ...

Global exponential stability is the most desirable stability property of recurrent neural networks. The paper presents new results for recurrent neural networks applied to online computation of feedback gains of linear time-invariant multivariable systems via pole assignment. The theoretical analysis focuses on the global exponential stability, convergence rates, and selection of design paramet...