⎯The problem of the global exponential stability of a class of Hopfield neural networks is considered. Based on nonnegative matrix theory, a sufficient condition for the existence, uniqueness and global exponential stability of the equilibrium point is presented. And the upper bound for the degree of exponential stability is given. Moreover, a simulation is given to show the effectiveness of th...

In this paper, we discuss delayed periodic dynamical systems, compare capability of criteria of global exponential stability in terms of various L (1 ≤ p < ∞) norms. A general approach to investigate global exponential stability in terms of various L (1 ≤ p < ∞) norms is given. Sufficient conditions ensuring global exponential stability are given, too. Comparisons of various stability criteria ...

In this paper we show that uniformly global asymptotic stability for a family of ordinary differential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change of variables. The same is shown for input-to-state stability and input-to-state exponential stability, and for input-to-state exponential stability and a nonlinear H∞ estimate.

We show that uniformly global asymptotic stability and input-to-state stability for a family of ordinary diierential equations are equivalent to uniformly global exponential stability and a nonlinear H1 estimate, respectively , under suitable nonlinear changes of variables.

This paper concerns the global stability of recently proposed laws for network congestion control. In earlier work it was shown that such laws were able to maintain local dynamic stability on networks of arbitrary delay, capacity and topology. In this paper we give conditions under which the stability can be shown to be global, focusing on the case of a single bottleneck network. The results in...

We present a global stability analysis of a Curzon–Ahlborn heat engine considering different regimes of performance. The stability theory is used to construct the Lyapunov functions to prove the asymptotic stability behavior around the steady state of internal temperatures. We provide a general analytic procedure for the description of the global stability by considering internal irreversibilit...

The stability of large distributed systems plays an important role in fault tolerance. However, it is generally difficult to evaluate the distributed stability in practice. This paper proposes to divide the stability into node stability and global stability. The node stability depicts the correct routing information acquired by a node due to network change, for example: node failure or leave. T...

We show that uniformly global asymptotic stability for a family of ordinary diierential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change of variables.