This paper focuses on the synchronization of reaction-diffusion complex dynamical networks with coupling delay. In order to reflect the uncertainties of the controller, the nonfragile problem is considered. Furthermore, we also take into account the dissipativity analysis problem, which contains the $$\cal{H}_{\infty}$$ performance and passivity performance in a unified framework. By utilizing the Lyapunov functional method, two sufficient delay-dependent conditions, which ensure the considered system is globally asymptotically synchronized onto the unforced node and strictly dissipative, are established in terms of linear matrix inequality. Finally, three numerical examples are employed to demonstrate the effectiveness of the design methods.

中文翻译：

---

具有耦合延迟的反应扩散复杂动力网络的非脆弱耗散同步

本文重点研究具有耦合延迟的反应扩散复杂动力网络的同步。为了反映控制器的不确定性，考虑了非脆弱性问题。此外，我们还考虑了耗散分析问题，该问题包含统一框架中的 $$\cal{H}_{\infty}$$ 性能和被动性能。利用李雅普诺夫泛函方法，根据线性矩阵不等式建立了两个充分的时滞相关条件，确保所考虑的系统全局渐近同步到非受迫节点上并严格耗散。最后，通过三个数值例子证明了设计方法的有效性。