Robustness Analysis for Connection Weight Matrices of Global Exponential Stability of Stochastic Delayed Recurrent Neural Networks

摘要

In this paper, we analyze the robustness of global exponential stability of stochastic delayed recurrent neural networks (SDRNNs) subject to parameter uncertainties in connection weight matrices. Given a globally exponentially stable SDRNN, the problem to be addressed here is how much the parameter uncertainties in connection weight matrices the SDRNN can withstand to be globally exponentially stable. Different from the traditional Lyapuvon stability theory, we only use the coefficients of global exponential stability. The upper bounds of parameter uncertainties are characterized using transcendental equations for the SDRNNs to sustain globally exponentially stable. Moreover, we prove theoretically that, for any globally exponentially stable SDRNNs, if additive parameter uncertainties in connection weight matrices are smaller than the derived upper bounds at here, then the perturbed SDRNNs are guaranteed to also be globally exponentially stable. A numerical example is provided here to illustrate the theoretical results.