An overview is given of the locally positive stabilization problem for positive infinite-dimensional linear systems with a bounded control operator. The impossibility of solving this problem by using a nonnegative input is established. Two methods for solving the problem by means of state feedback, namely spectral decomposition and control invariance, are described. The results are illustrated by means of a perturbed diffusion equation with Dirichlet boundary conditions and a diffusion equation with Neumann boundary conditions and pointwise control.

中文翻译：

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基于状态反馈的无限维线性系统的局部正稳定

概述了具有有界控制算子的正无限维线性系统的局部正稳定问题。通过使用非负输入来解决这个问题是不可能的。描述了利用状态反馈解决问题的两种方法，即谱分解和控制不变性。结果通过带有 Dirichlet 边界条件的扰动扩散方程和带有 Neumann 边界条件和逐点控制的扩散方程来说明。