论文标题
在通用类别的Lyapunov函数上，用于线性开关系统
On universal classes of Lyapunov functions for linear switched systems
论文作者
论文摘要
在本文中，我们讨论了线性开关系统的候选lyapunov函数类别的普遍性概念。一方面，我们证明，一家绝对同质功能的家族在任意近似于单位球体的$ c^0 $拓扑的每个凸的绝对均匀函数时就会普遍存在。另一方面，我们证明了一个班级是普遍的障碍，特别是表明分段多项式连续功能的家庭最多涉及$ l $ lughtimials of $ m $的构造（对于鉴定的正整数$ l，m $）是不普遍的。
In this paper we discuss the notion of universality for classes of candidate common Lyapunov functions of linear switched systems. On the one hand, we prove that a family of absolutely homogeneous functions is universal as soon as it approximates arbitrarily well every convex absolutely homogeneous function for the $C^0$ topology of the unit sphere. On the other hand, we prove several obstructions for a class to be universal, showing, in particular, that families of piecewise-polynomial continuous functions whose construction involves at most $l$ polynomials of degree at most $m$ (for given positive integers $l,m$) cannot be universal.
