Localization of Compact Invariant Sets of Discrete-Time Systems with Disturbances

被引：7
|
作者：
Kanatnikov, A. N. [1 ]
Korovin, S. K. [2 ]
Krishchenko, A. P. [1 ,2 ]
机构：
[1] Bauman State Tech Univ, Moscow 105005, Russia
[2] Russian Acad Sci, Inst Syst Anal, Moscow 117312, Russia
来源：
DOKLADY MATHEMATICS | 2011年 / 83卷 / 03期
基金：
俄罗斯基础研究基金会;
关键词：
Phase Space; DOKLADY Mathematic; Discrete Time System; Inverse System; Intersection Theorem;
D O I：
10.1134/S1064562411030392
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A method for constructing localizing sets for discrete-time systems with disturbances is proposed and the properties of localizing sets are established. Conditions for the existence of maximal invariant compact sets for a discrete-time system with disturbances are obtained and a method for finding such sets is suggested. It is proved that any positively invariant compact set of system that is contained in a set also contained in the set. A necessary and sufficient condition for negative invariance with the additional compactness condition is stated. For systems with disturbances, there are analogues of properties of undisturbed discrete-time systems associated with shifts of localizing sets along trajectories of the system. For a compact set, the corresponding set is the maximal positively invariant compact set of system among the positively invariant compact sets contained in G.
引用
收藏
页码：433 / 435
页数：3
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