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.

对于由不同节点组成的耦合神经网络（CNNs），本文解决了\(\mathcal {H}_\infty \)同步和鲁棒\(\mathcal {H}_\infty \)同步问题. 一方面，通过利用 Lyapunov 函数策略和一些不等式技术，获得了一些新的\(\mathcal {H}_\infty \)同步标准，用于由具有相同维度的不同节点组成的 CNN。同时，考虑到外部干扰很可能在 CNNs 建模过程中产生不确定参数，我们还研究了鲁棒性\(\mathcal {H}_\infty \)具有参数不确定性的考虑的神经网络的同步。此外，给出了几个新条件来保证在合适的钉扎自适应下考虑的神经网络的钉扎自适应\(\mathcal {H}_\infty \)同步和鲁棒钉扎自适应\(\mathcal {H}_\infty \)同步法律。另一方面，研究了由不同维度的不同节点组成的 CNN 的\(\mathcal {H}_\infty \)同步和鲁棒\(\mathcal {H}_\infty \)同步分析和钉扎控制相似地。最后，给出两个例子来展示导出的\(\mathcal {H}_\infty \)同步和鲁棒性的有效性\(\mathcal {H}_\infty \)同步条件。