Linear proportional ISS synthesis of parabolic systems is developed within the practical framework of in-domain embedded sensing and actuation. The underlying system is affected by external disturbances and it is governed by a non-homogeneous reaction–diffusion PDE with a priori unknown spatially varying parameters. The present investigation focuses on practically motivated sampled-in-space sensing and actuation. A finite number of available sensing and actuating devices are assumed to be located along the one-dimensional spatial domain of interest. Tuning of the controller gains is then constructively developed by means of the Lyapunov approach to achieve a desired attenuation level for external distributed disturbances, affecting the system in question. Dual observer design is additionally developed within the present framework, and it is involved into the non-collocated output feedback synthesis. Theoretical results are supported by simulations made for the proposed synthesis over non-collocated sensing and actuation.

抛物线型系统的线性比例ISS合成是在域内嵌入式感应和驱动的实际框架内开发的。底层系统受到外部干扰的影响，并且受具有先验性的非均匀反应扩散PDE的支配未知的空间变化参数。本研究侧重于实际动机的空间采样传感和驱动。假定沿感兴趣的一维空间域定位了有限数量的可用传感和致动设备。然后，通过Lyapunov方法建设性地开发控制器增益的调谐，以实现所需的外部分布式干扰的衰减水平，从而影响所讨论的系统。在本框架内还开发了双观察器设计，并且该双观察器设计涉及非并置输出反馈综合。理论结果得到了在非并置传感和驱动下对拟议综合进行仿真的支持。