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

页码：433 / 435

页数：3

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