论文标题
线性开关系统的稳定性半径的下限和密集的不连续性现象
Lower bounds and dense discontinuity phenomena for the stabilizability radius of linear switched systems
论文作者
论文摘要
我们研究了离散时间线性切换系统的稳定性，当控制器的唯一控制动作是开关信号时，以及当控制器可以实时访问系统状态时。尽管它们显然很简单，但确定该系统是否可以稳定似乎是一个非常具有挑战性的问题，并且长期以来已经知道了基本示例，为此，稳定性问题是开放的。我们提供了新的结果，使我们能够绑定所谓的稳定性半径，该半径是离散时间线性开关系统的稳定性属性的特征。这些结果使我们能够在上述示例上显着改善稳定性半径上的明确下限。作为副产品，我们表现出该问题的不连续性，这对其复杂性带来了理论上的理解。
We investigate the stabilizability of discrete-time linear switched systems, when the sole control action of the controller is the switching signal, and when the controller has access to the state of the system in real time. Despite their apparent simplicity, determining if such systems are stabilizable appears to be a very challenging problem, and basic examples have been known for long, for which the stabilizability question is open. We provide new results allowing us to bound the so-called stabilizability radius, which characterizes the stabilizability property of discrete-time linear switched systems. These results allow us to compute significantly improved explicit lower bounds on the stabilizability radius for the above-mentioned examples. As a by-product, we exhibit a discontinuity property for this problem, which brings theoretical understanding of its complexity.
