This study considers the passivity of fractional reaction-diffusion systems (FRDSs) featuring boundary input-output. The fundamental framework for this exploration involves the application of the Lyapunov-Krasovskii functional method coupled with inequality techniques. The investigation derives sufficient conditions that guarantee both input and output strict passivity in FRDSs. Furthermore, in the presence of fluctuating uncertain parameters within FRDSs, robust passivity is also studied and sufficient conditions are offered. The obtained sufficient condition shows that a larger diffusion coefficient facilitates the achievement of the passivity of FRDSs. Finally, the validity of our theoretical findings is subsequently corroborated through numerical examples.

中文翻译：

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分级反应扩散系统的被动性


本研究考虑了具有边界输入-输出特征的分数反应扩散系统（FRDS）的被动性。这一探索的基本框架涉及 Lyapunov-Krasovskii 泛函方法与不等式技术的应用。研究得出了保证 FRDS 中输入和输出严格无源性的充分条件。此外，在FRDS中存在波动的不确定参数的情况下，还研究了鲁棒无源性并提供了充分的条件。得到的充分条件表明，较大的扩散系数有利于FRDS实现无源性。最后，我们的理论研究结果的有效性随后通过数值例子得到证实。