Synchronization criteria for neural networks with proportional delays via quantized control

With the aid of quantized control, this paper presents new synchronization criteria of neural networks (NNs) with proportional delays. The NNs with constant delays and variable coefficients are obtained, which are equivalently transformed from the NNs with proportional delays. Taking the communication limitation into account, quantized controllers which include state feedback controllers and quantized adaptive controllers are designed for the first time for solving synchronization problem of NNs with proportional delays. By constructing Lyapunov function, utilizing new controllers, and applying new analytical methods, several criteria are derived to realize synchronization. Here, the obtained synchronization of NNs with proportional delays is not called exponential synchronization since the convergence rate is not fixed. Finally, numerical simulations are offered to substantiate our theoretical results.

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