The dynamic H∞ feedback boundary control for a class of parabolic distributed parameter systems with a non-constant (spatially varying) diffusion rate is addressed in this paper. The observer-based controller is designed to deal with non-collocated sensors and actuators, and the H∞ performance index is employed to tackle the influence of the external disturbance and measurement noise. The resulting closed-loop system is formed by the boundary actuation with the H∞ control strategy, and the output feedback is designed from the domain-averaged and boundary-valued measurement, respectively. With the sufficient conditions of the linear matrix inequality that infer the stability of the system, the corresponding gains of observer and controller are solved. Numerical simulations are given to show the validity of the main results.

中文翻译：

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一类具有空间变化扩散率的抛物线系统的动态H∞，反馈边界控制

本文讨论了一类具有非恒定（空间变化）扩散率的抛物线分布参数系统的动态 H∞ 反馈边界控制。基于观测器的控制器设计用于处理非并置的传感器和执行器，并采用 H∞ 性能指标来解决外部干扰和测量噪声的影响。由此产生的闭环系统由具有 H∞ 控制策略的边界驱动形成，输出反馈分别由域平均和边界值测量设计。利用推断系统稳定性的线性矩阵不等式的充分条件，求解观测器和控制器的相应增益。数值模拟显示了主要结果的有效性。