A SIR epidemic model with delay, saturated contact rate and vertical transmission is considered. The basic reproduction number 0 R is calculated. It is shown that this number characterizes the disease transmission dynamics: if 0 1 R , there only exists the disease-free equilibrium which is globally asymptotically stable; if 0 1 R , there is a unique endemic equilibrium and the disease persists,...

In this paper we present a suucient condition for master-slave synchronization of Lur'e systems. The scheme makes use of linear full static state feedback. The criterion is based on a Lur'e-Postnikov Lyapunov function for global asymptotic stability of the error system. The condition is basically the same as the one for global asymptotic stability of the Lur'e system, controlled with linear sta...

In this paper, we obtain the global asymptotic stability of the zero solution of a general n-dimensional delayed differential system, by imposing a condition of dominance of the nondelayed terms which cancels the delayed effect. We consider several delayed differential systems in general settings, which allow us to study, as subclasses, the well known neural network models of Hopfield, CohnGros...

A converse Lyapunov theorem is established for discrete-time stochastic systems with non-unique solutions. In order to prove the result, mild regularity conditions are imposed on the set-valued mapping that characterizes the update of the system state. It is shown that global asymptotic stability in probability implies the existence of a continuous Lyapunov function, smooth outside of the attra...

Global asymptotic stability of rational difference equations is an area of research that has been well studied. In contrast to the many current methods for proving global asymptotic stability, we propose an algorithmic approach. The algorithm we summarize here employs the idea of contractions. Given a particular rational difference equation, defined by a function Q : R → R, we attempt to find a...

We consider global stability of a flow network model for vehicular traffic. Standard approaches which rely on monotonicity of flow networks for stability analysis do not immediately apply to traffic networks with diverging junctions. In this paper, we show that the network model nonetheless exhibits a mixed monotonicity property. Mixed monotonicity allows us to prove global asymptotic stability...

This paper presents a consensus-based formation control scheme for autonomous multi-agent systems represented by double integrator dynamics. Assuming that the information graph topology consists of an undirected connected graph, a leader-based consensus-type control law is presented and shown to provide asymptotic formation stability when subjected to piecewise constant formation velocity comma...

This paper presents an experimental analysis of a recently proposed decentralized control strategy, for collective circular motion of a team of nonholonomic vehicles. Theoretical results ensuring global asymptotic stability in the single-vehicle case and local asymptotic stability in the multi-vehicle scenario, are validated on an experimental setup including the mobile robots Pioneer 3AT and N...

We consider asymptotic stability of a small solitary wave to supercritical 2-dimensional nonlinear Schrödinger equations iut +∆u = V u± |u|u for (x, t) ∈ R × R, in the energy class. This problem was studied by Gustafson-NakanishiTsai [14] in the n-dimensional case (n ≥ 3) by using the endpoint Strichartz estimate. Since the endpoint Strichartz estimate fails in 2-dimensional case, we use a time...

We present several equivalent characterizations of uniform global exponential stability (UGES) and uniform global asymptotic stability (UGAS) of arbitrary closed (not necessarily compact) sets for nonlinear difference inclusions. In particular, we provide several characterizations of these stability properties via summability criteria that do not require the knowledge of a Lyapunov function. We...