This paper considers the asymptotic stability analysis of both exact and numerical solutions of the following neutral delay differential equation with pantograph delay. ⎧⎨ ⎩ x′(t) +Bx(t) + Cx′(qt) +Dx(qt) = 0, t > 0, x(0) = x0, where B,C,D ∈ Cd×d, q ∈ (0, 1), and B is regular. After transforming the above equation to non-automatic neutral equation with constant delay, we determine sufficient co...

New tests for checking asymptotic stability of positive 1D continuous-time and discrete-time linear systems without and with delays and of positive 2D linear systems described by the general and the Roesser models are proposed. Checking of the asymptotic stability of positive 2D linear systems is reduced to checking of suitable corresponding 1D positive linear systems. It is shown that the stab...

In this paper we first study the problem of practical asymptotic stability for a class of discrete-time time-delay systems via Razumikhin-type Theorems. Further the estimations of solution boundary and arrival time of the solution into a region are also investigated based on the practical stability results. Finally, the result on practical asymptotic stability is used to analyze the practical c...

We consider a single-link multi-source network with FAST TCP sources. We adopt a continuous-time dynamic model for FAST TCP sources, and propose a static model to adequately describe the queuing delay dynamics at the link. The proposed model turns out to have a structure that reveals the time-varying network feedback delay, which allows us to analyze FAST TCP with due consideration of the time-...

The main focus of the paper is on the asymptotic behaviour of linear discrete-time positive systems. Emphasis is on highlighting the relationship between asymptotic stability and the structure of the system, and to expose the relationship between null-controllability and asymptotic stability. Results are presented for both time-invariant and time-variant systems.

We present sufficient conditions for global asymptotic stability of cascade discrete-time systems. Considering failure of the global asymptotic stability in some cascade systems, we give an estimate of the region of attraction of the systems.

K e y w o r d s N o n l i n e a r systems, Cascade systems, Discrete-time systems~ Local asymptotic stability, Global asymptotic stability.

This paper presents new analytical results on the global asymptotic stability for the equilibrium states of a general class of discrete-time recurrent neural networks (DTRNNs) described by using a set of nonlinear di erence equations. We provide a few suÆcient conditions for the global asymptotic stability of DTRNNs. The resulting criteria include diagonal stability and nondiagonal stability. T...

In the present paper a generalized Lotka-Volterra food chain system has been studied and also its dynamic behavior such as locally asymptotic stability has been analyzed in case of existing interspecies competition. Furthermore, it has been shown that the said system is permanent (in the sense of boundedness and uniformly persistent). Finally, it is proved that the nontrivial equilibrium point...

Retrial phenomenon naturally arises in various systems such as call centers, cellular networks and random access protocols in local area networks. This paper gives a comprehensive survey on theory and applications of retrial queues in these systems. We investigate the state of the art of the theoretical researches including exact solutions, stability, asymptotic analyses and multidimensional mo...