线性控制系统的无界多面体不变集

摘要

The nonsmooth analysis methods are applied to investigate the unbounded polyhedral invariant sets for linear control systems. When the extreme directions of an unbounded polyhedron satisfy some conditions, we derive the criterion for that unbounded polyhedron to be a weak invariant set for a class of linear control systems. The sufficient condition is also obtained for the unbounded polyhedron to be the strong invariant set for more general linear control systems. Two applied examples are given for illustration.%本文利用非光滑分析方法,讨论了线性控制系统的无界多面体不变集问题.当无界多面体的极方向满足一定条件时,得到了该无界多面体为一类线性控制系统弱不变集的判别方法.然后在更一般的线性控制系统下给出了无界多面体为强不变集的充分条件.最后给出两个应用实例.