Title
Effect of transmission delay on the rate of convergence of a class of nonlinear contractive dynamical systems
Document Type
Letter to the Editor
Publication Date
1-1-2002
Abstract
We investigate the qualitative properties of a general class of contractive dynamical systems with time delay by using a unified analysis approach for any p-contraction with p ∈ [1, ∞]. It is proved that the delayed contractive dynamical system is always globally exponentially stable no matter how large the time delay is, while the rate of convergence of the delayed system is reduced as the time delay increases. A lower bound on the rate of convergence of the delayed contractive dynamical system is obtained, which is the unique positive solution of a nonlinear equation with three parameters, namely, the time delay, the time constant and the p-contraction constant in the system. We show that the previously established results in the literature about the global asymptotic or exponential stability independent of delay for Hopfield-type neural networks can actually be deduced by recasting the network model into the general framework of contractive dynamical systems with some p-contraction (p ∈ [1, ∞]) under the given-delay-independent stability conditions. Numerical simulation examples are also presented to illustrate the obtained theoretical results.
Publication Source (Journal or Book title)
IEEE Transactions on Neural Networks
First Page
244
Last Page
248
Recommended Citation
Liang, X. (2002). Effect of transmission delay on the rate of convergence of a class of nonlinear contractive dynamical systems. IEEE Transactions on Neural Networks, 13 (1), 244-248. https://doi.org/10.1109/72.977316