The finite-time control is considered for reaction–diffusion systems (RDSs) under a designed spatial sampled-data controller (SSDC). Firstly, an SSDC is designed and the finite-time stability is investigated for RDSs, based on the designed controller. In terms on Lyapunov functional method and inequality techniques, a sufficient condition is obtained to ensure the finite-time stability. Then, uncertain RDSs are studied and the robust finite-time stability is considered. Under the designed SSDC, a criterion is obtained to ensure the uncertain RDSs to achieve robust finite-time stability. When there exist external disturbances, the \(H_\infty \) performance of RDSs is investigated. Both distributed disturbances and boundary disturbances are considered, and sufficient conditions are obtained to guarantee the finite-time \(H_\infty \) performance with the designed SSDC. Finally, examples are given to verify the effectiveness of our theoretical results.

在设计的空间采样数据控制器（SSDC）下考虑反应扩散系统（RDS）的有限时间控制。首先，基于所设计的控制器，设计了SSDC并研究了RDS的有限时间稳定性。在Lyapunov泛函方法和不等式技术方面，得到了保证有限时间稳定性的充分条件。然后，研究了不确定的RDS，并考虑了鲁棒的有限时间稳定性。在设计的SSDC下，获得了一个准则，以确保不确定的RDSs实现鲁棒的有限时间稳定性。当存在外部干扰时，\(H_\infty \)RDS 的性能进行了研究。考虑了分布式扰动和边界扰动，并获得了充分条件以保证所设计的 SSDC的有限时间\(H_\infty \)性能。最后，通过实例验证了我们理论结果的有效性。