论文标题
通过模态分解（扩展版）的线性抛物线系统的内部稳定
Internal stabilization of an underactuated linear parabolic system via modal decomposition (extended version)
论文作者
论文摘要
这项工作涉及级联$ M $热方程的线性系统不足的内部稳定，在该系统内部仅将控件放置在第一个方程式中，并且扩散系数是不同的。将模态分解方法与最近引入的观察问题的状态转化方法相结合，明确给出了比例类型的稳定控制。它基于与相对不稳定模式相对应的ODE系统的转换，在该模式下，稳定定律的计算独立于任意数量的数量，并且可以通过递归解决通用的Sylvester方程来实现。这提供了最近引入的无限维度的有限维度对应物，从而导致Lyapunov稳定。目前的方法回答了稳定问题的问题，而执行器并非所有州出现，并且何时不适用边界控制结果。
This work concerns the internal stabilization of underactuated linear systems of $m$ heat equations in cascade, where the control is placed internally in the first equation only and the diffusion coefficients are distinct. Combining the modal decomposition method with a recently introduced state-transformation approach for observation problems, a proportional-type stabilizing control is given explicitly. It is based on a transformation for the ODE system corresponding to the comparatively unstable modes into a target one, where calculation of the stabilization law is independent of the arbitrarily large number of them and it is achieved by solving generalized Sylvester equations recursively. This provides a finite-dimensional counterpart of a recently introduced infinite-dimensional one, which led to Lyapunov stabilization. The present approach answers to the problem of stabilization with actuators not appearing in all the states and when boundary control results do not apply.
