切换系统多面体区域的生存性判别
Determining the viability of a polytope for a switched system

本文研究了切换系统关于多面体区域的生存性判别问题. 考虑多面体由有限点集凸包来表示, 利用非光滑 分析理论, 得到一个切换系统生存性的充分条件. 该条件只需检验在极点处是否满足特定条件, 而不需要对每个边 界点进行验证. 其优点在于将生存性的判别转化为向量内积与切锥的计算. 这种生存性判别方法简便易行. 最后通 过实例阐述了算法的有效性.
This paper is devoted to the viability criterion for a polytope under a switched system. A sufficient viability criterion for a polytope, which is expressed by a convex hull of finite number of points, is proposed by using nonsmooth analysis. Based on this criterion, instead of all boundary points, just several vertices are needed to be verified whether satisfying some conditions. The advantage of the proposed methods is that determining the viability is transformed into computing vectors inner product and tangents. This method of determining the viability is easy to be complemented. Finally, two examples are listed to illustrate the effectiveness of main results of this paper.