Common diagonal solutions to the Lyapunov inequalities for interval systems

被引：0
|
作者：
Bengi Yıldız
Taner Büyükköroğlu
Vakif Dzhafarov
机构：
[1] Bilecik Seyh Edebali University,Department of Mathematics
[2] Anadolu University,Department of Mathematics
来源：
Journal of Inequalities and Applications | / 2016卷
关键词：
interval matrices; Lyapunov inequality; diagonal stability; common diagonal solution; minimax problem;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper for interval systems we consider the problem of existence and evaluation of common diagonal solutions to the Lyapunov inequalities. For second order systems, we give necessary and sufficient conditions and exact solutions, that is, complete theoretical solutions. For third order systems, an algorithm for the evaluation of common solutions in the case of existence is given. In the general case a sufficient condition is obtained for a common diagonal solution in terms of the center and upper bound matrices of an interval family.
引用
收藏
相关论文
共 50 条
  • [1] Common diagonal solutions to the Lyapunov inequalities for interval systems
    Yildiz, Bengi
    Buyukkoroglu, Taner
    Dzhafarov, Vakif
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016,
  • [2] On common diagonal Lyapunov solutions
    Gumus, Mehmet
    Xu, Jianhong
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2016, 507 : 32 - 50
  • [3] Block-Diagonal Solutions to Lyapunov Inequalities and Generalisations of Diagonal Dominance
    Sootla, Aivar
    Zheng, Yang
    Papachristodoulou, Antonis
    [J]. 2017 IEEE 56TH ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC), 2017,
  • [4] Interval systems - Construction and Exploitation of Diagonal Lyapunov Functions
    Pastravanu, Octavian
    Matcovschi, Mihaela-Hanako
    Voicu, Mihail
    [J]. 2015 19TH INTERNATIONAL CONFERENCE ON SYSTEM THEORY, CONTROL AND COMPUTING (ICSTCC), 2015, : 13 - 18
  • [5] On the Existence of Block-Diagonal Solutions to Lyapunov and H∞ Riccati Inequalities
    Sootla, Aivar
    Zheng, Yang
    Papachristodoulou, Antonis
    [J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2020, 65 (07) : 3170 - 3175
  • [6] DIAGONAL COMMON QUADRATIC LYAPUNOV FUNCTIONS FOR SETS OF POSITIVE LTI SYSTEMS
    Liu, Xiu
    Shu, Lan
    Ding, Xiuyong
    [J]. MISKOLC MATHEMATICAL NOTES, 2014, 15 (02) : 593 - 602
  • [7] On diagonal common quadratic Lyapunov functions for sets of homogeneous cooperative systems
    Ding, Xiuyong
    Shu, Lan
    Liu, Xiu
    [J]. AEQUATIONES MATHEMATICAE, 2013, 85 (03) : 231 - 241
  • [8] On diagonal common quadratic Lyapunov functions for sets of homogeneous cooperative systems
    Xiuyong Ding
    Lan Shu
    Xiu Liu
    [J]. Aequationes mathematicae, 2013, 85 : 231 - 241
  • [9] Systems of diagonal Diophantine inequalities
    Freeman, E
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 355 (07) : 2675 - 2713
  • [10] On Existence of Solutions to Structured Lyapunov Inequalities
    Sootla, Aivar
    Anderson, James
    [J]. 2016 AMERICAN CONTROL CONFERENCE (ACC), 2016, : 7013 - 7018
12345