Stability analysis of some delay differential inequalities with small time delays and its applications
In this paper, we discuss the asymptotic stability of the trajectories governed by the scalar delay differential inequalities: D(+)x(t)   is small, the asymptotic stability of x(t) can be obtained if the time average of a(t) - b(t) on some fixed length T is lower bounded by some positive delta. And we explicitly give the upper bound of (tau) over bar .We also give two applications of the theoretical results. First, we consider self synchronization in Hopfield networks with time varying connections. Then we investigate consensus in networks with time varying topologies and arbitrary coupling weights. In both applications, we extend some of our previous works where time delays are not considered. At last, two numerical examples with simulations are provided to illustrate the effectiveness of the theoretical results. (c) 2012 Elsevier Ltd. All rights reserved.
delay differential inequality asymptotic stability time varying systems neural networks