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
相关论文
共 50 条
  • [41] POSITIVELY INVARIANT POLYHEDRAL-SETS OF DISCRETE-TIME LINEAR-SYSTEMS
    BITSORIS, G
    INTERNATIONAL JOURNAL OF CONTROL, 1988, 47 (06) : 1713 - 1726
  • [42] On the Convergence of the Backward Reachable Sets of Robust Controlled Invariant Sets For Discrete-time Linear Systems
    Liu, Zexiang
    Ozay, Necmiye
    2022 IEEE 61ST CONFERENCE ON DECISION AND CONTROL (CDC), 2022, : 4270 - 4275
  • [43] Positively invariant polyhedral sets for discrete-time singular systems with additive perturbations
    Castelan, EB
    Tarbouriech, S
    PROCEEDINGS OF THE 35TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-4, 1996, : 992 - 993
  • [44] Localization of Compact Invariant Sets for Continuous-time Nonlinear Systems with Uncertainties
    Kanatnikov, A. N.
    Krishchenko, A. P.
    PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2016 (ICNAAM-2016), 2017, 1863
  • [45] Localization of Invariant Compact Sets for Continuous Systems with Uncertainties
    Kanatnikov A.N.
    Krishchenko A.P.
    Journal of Mathematical Sciences, 2016, 219 (1) : 150 - 154
  • [46] Computation of invariant sets for piecewise affine discrete time systems subject to bounded disturbances
    Rakovic, SV
    Grieder, P
    Kvasnica, M
    Mayne, DQ
    Morari, M
    2004 43RD IEEE CONFERENCE ON DECISION AND CONTROL (CDC), VOLS 1-5, 2004, : 1418 - 1423
  • [47] Computation of controlled invariant sets for discrete-time switched nonlinear systems with time-delay
    Chen, Ruijuan
    Li, Yinan
    Liu, Jun
    JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2021, 358 (14): : 7187 - 7202
  • [48] Asymptotic Controllability of Discrete-time Systems with Disturbances
    Cai, Xiushan
    Lv, Ganyun
    Xu, Xiuling
    He, Xiuhui
    2008 CHINESE CONTROL AND DECISION CONFERENCE, VOLS 1-11, 2008, : 4189 - 4192
  • [49] On Robustly Positively Invariant Sets and Coordinate Transformations for Discrete-time Nonlinear Systems: a Tutorial
    Kaldmaee, Arvo
    De Dona, Jose
    2019 AUSTRALIAN & NEW ZEALAND CONTROL CONFERENCE (ANZCC), 2019, : 24 - 29
  • [50] Reachability analysis of discrete-time systems with disturbances
    Rakovic, SV
    Kerrigan, EC
    Mayne, DQ
    Lygeros, J
    IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2006, 51 (04) : 546 - 561
12345