Let G be a graph and f: G → G be continuous. Denote by R(f) and Ω(f) the set of recurrent points and the set of non-wandering points of f respectively. Let Ω0 (f) = G and Ωn (f) =Ω(f|Ωn-1(f)) for all n ∈ N. The minimal m ∈ NU {∞} such that Ωm(f) = Ωm+1(f) is called the depth of f. In this paper, we show that Ω2(f) = R(f) and the depth of f is at most 2. Furthermore, we obtain some properties of non-wandering points of f.
Jie-hua MAI~1 Tai-xiang SUN~(2+) ~1 Institute of Mathematics,Shantou University,Shantou 515063,China
This paper considers the guaranteed cost control problem for a class of uncertain linear systems with both state and input delays.By representing the time-delay system in the descriptor system form and using a recent result on bounding of cross products of vectors,we obtain new delay-dependent sufficient conditions for the existence of the guaranteed cost controller in terms of linear matrix inequalities.Two examples are presented which show the effectiveness of our approach.
