In this paper, we consider boundary stabilization problem of heat equation with multi-point heat source. Firstly, a state feedback controller is designed mainly by backstepping approach. Under the designed state controller, the exponential stability of closed-loop system is guaranteed. Then, an observer-based output feedback controller is proposed. We prove the exponential stability of resulting closed-loop system using operator semigroup theory. Finally, the designed state and output feedback controllers are effective via some numerical simulations.

中文翻译：

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多点热源热方程的边界稳定

在本文中，我们考虑了具有多点热源的热方程的边界稳定问题。首先，主要通过反步法设计状态反馈控制器。在设计的状态控制器下，保证了闭环系统的指数稳定性。然后，提出了一种基于观察者的输出反馈控制器。我们使用算子半群理论证明了所得闭环系统的指数稳定性。最后，通过一些数值模拟，所设计的状态和输出反馈控制器是有效的。