We propose a constructive design method for linear systems with a non-trivial drift term, guaranteeing robust global asymptotic stability of the origin of the closed-loop system, as well as robust obstacle avoidance. To obtain discontinuous input actions, our controller is designed in the framework of hybrid systems. Using our proposed hybrid controller, we demonstrate that solutions do not enter a sphere, which we term an avoidance neighborhood, around specified isolated points. The constructive controller design methodology, as well as the closed-loop properties, are investigated via numerical examples.

中文翻译：

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具有漂移的线性系统的稳定鲁棒回避控制器的显式构造

我们提出了一种具有非平凡漂移项的线性系统的建设性设计方法，保证闭环系统原点的鲁棒全局渐近稳定性，以及鲁棒的避障。为了获得不连续的输入动作，我们的控制器是在混合系统的框架中设计的。使用我们提出的混合控制器，我们证明了解决方案不会进入指定孤立点周围的球体，我们称之为回避邻域。通过数值例子研究了构造控制器设计方法以及闭环特性。