We consider a possible application of the Ważewski topological method to feedback control systems and to more general dynamical systems. We show how this method can be used to prove the impossibility of global stabilization in such problems. Moreover, we give sufficient conditions for the existence of a solution such that its trajectory never leaves a subset of the extended phase space of the system and does not tend asymptotically to a given equilibrium. We illustrate our result with various real-life systems including the Furuta pendulum and the wheeled inverted pendulum.

中文翻译：

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Ważewski方法在整体稳定问题上的应用

我们考虑了Ważewski拓扑方法在反馈控制系统和更一般的动力学系统中的可能应用。我们展示了如何使用这种方法来证明在此类问题中不可能实现全球稳定。此外，我们为解的存在提供了充分的条件，以使它的轨迹不会离开系统扩展相空间的子集，并且不会渐近地趋于给定的平衡。我们用包括古田摆和轮式倒立摆在内的各种现实系统来说明我们的结果。