Effect of transmission delay on the rate of convergence of a classof nonlinear contractive dynamical systems
Xue-Bin Liang
Neural Networks, IEEE Transactions on
Volume 13, Issue 1, Jan 2002 Page(s):244 - 248
Digital Object Identifier 10.1109/72.977316
Summary: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
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