\(\mathcal {H}_\infty \) Synchronization and Robust \(\mathcal {H}_\infty \) Synchronization of Coupled Neural Networks with Non-identical Nodes

摘要

For coupled neural networks (CNNs) composed of non-identical nodes, the problems of \(\mathcal {H}_\infty \) synchronization and robust \(\mathcal {H}_\infty \) synchronization are solved in the paper. On the one side, some new \(\mathcal {H}_\infty \) synchronization criteria for CNNs consisting of non-identical nodes with the same dimensions are acquired by exploiting the Lyapunov functional strategy and some inequality techniques. Meanwhile, considering that external disturbances are likely to produce the uncertain parameters in the modeling process of CNNs, we also investigate robust \(\mathcal {H}_\infty \) synchronization for the considered neural network with parametric uncertainties. Furthermore, several new conditions are given to guarantee the pinning adaptive \(\mathcal {H}_\infty \) synchronization and robust pinning adaptive \(\mathcal {H}_\infty \) synchronization for considered neural networks under suitable pinning adaptive law. On the other side, \(\mathcal {H}_\infty \) synchronization and robust \(\mathcal {H}_\infty \) synchronization analysis and pinning control for CNNs consisting of non-identical nodes of different dimensions are investigated similarly. At the end, two examples are given to display the effectiveness of the derived \(\mathcal {H}_\infty \) synchronization and robust \(\mathcal {H}_\infty \) synchronization conditions.