Convergence Analysis of Recurrent Neural Networks by Zhang Yi

+oo = x*.

The details are thus omitted. The proof is completed. 4 Global Exponential Stability and Convergence Rate Estimation Global exponential stability (GES) is a good convergence property of dynamic systems. It can provide a dear understanding of the convergence, which is especially interesting in engineering field. 2). Meanwhile, the GES convergence rate estimation will also be given. 2) is ca lied GES, ifthere exist constants E > 0 and M ~ 1 such that forall t ~ O. 2) is GES. Moreover, for all t ~ 0 and (i = 1"" ,n), where _..

Finally in Seetion 6, conclusions follow to summarize this chapter. 2. Properties of Output function Tbe output function 1 of CNNs is defined as folIows: 1(8) = 18 + 11 ; 18 - 11, 8E R. ) is a piecewise linear function, which is continuous but non-differentiable. 1 shows this function. 1. Output function f of CNNs 1 is an important characteristic of CNNs. In fact, many dynamic properties and applications of CNNs are crucially dependent on its properties. In order to study the convergence of CNNs, it is necessary to study the properties of 1 first.

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