Spectral Conditions for Stability and Stabilization of Positive Equilibria for a Class of Nonlinear Cooperative Systems

被引：9
|
作者：
Abara, Precious Ugo [1 ,2 ]
Ticozzi, Francesco [1 ,3 ]
Altafini, Claudio [4 ]
机构：
[1] Univ Padua, Dept Informat Engn, I-35131 Padua, Italy
[2] Tech Univ Munich, D-80333 Munich, Germany
[3] Dartmouth Coll, Dept Phys & Astron, Hanover, NH 03755 USA
[4] Linkoping Univ, Dept Elect Engn, Div Automat Control, SE-58183 Linkoping, Sweden
来源：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2018年 / 63卷 / 02期
基金：
瑞典研究理事会;
关键词：
Concave systems; nonlinear cooperative systems; positive equilibrium points; stability and stabilization; subhomogeneous systems; PERRON-FROBENIUS THEOREM; POWER-CONTROL; NETWORKS; UNIQUENESS; DYNAMICS;
D O I：
10.1109/TAC.2017.2713241
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Nonlinear cooperative systems associated to vector fields that are concave or subhomogeneous describe well interconnected dynamics that are of key interest for communication, biological, economical, and neural network applications. For this class of positive systems, we provide conditions that guarantee existence, uniqueness and stability of strictly positive equilibria. These conditions can be formulated directly in terms of the spectral radius of the Jacobian of the system. If control inputs are available, then it is shown how to use state feedback to stabilize an equilibrium point in the interior of the positive orthant.
引用
收藏
页码：402 / 417
页数：16
相关论文
共 50 条
  • [41] Stabilization of a Class of Stochastic Nonlinear Systems
    Ghaffari, Valiollah
    Karimi, Hamid Reza
    Noroozi, Navid
    Naghavi, S. Vahid
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2013, 2013
  • [42] Robust Stabilization for A Class of Nonlinear Systems
    Cai, Xiushan
    Lin, Rong
    Su, Shaoqing
    2008 CHINESE CONTROL AND DECISION CONFERENCE, VOLS 1-11, 2008, : 4840 - 4844
  • [43] Stabilization of Nonlinear Homogeneous and Cooperative Delay Systems
    Dastyar, Fateme
    Keyanpour, Mohammad
    PROCEEDINGS OF 2019 15TH IRAN INTERNATIONAL INDUSTRIAL ENGINEERING CONFERENCE (IIIEC), 2019, : 239 - 242
  • [44] Stability Analysis of a Class of Nonlinear Systems with Delays: A Positive System Method
    Liu, Xingwen
    Yang, Jinxiang
    Wang, Xiaoling
    2017 CHINESE AUTOMATION CONGRESS (CAC), 2017, : 1625 - 1629
  • [45] A Necessary and Sufficient Condition for Stability of a Class of Planar Positive Nonlinear Systems
    Zou, Yunlei
    Qian, Chunjiang
    IEEE CONTROL SYSTEMS LETTERS, 2021, 5 (02): : 535 - 540
  • [46] Stability and Stabilization of Fuzzy Event-Triggered Control for Positive Nonlinear Systems
    Wang, Ziguang
    Meng, Aiwen
    Lam, Hak-Keung
    Xiao, Bo
    Li, Zhiquan
    INTERNATIONAL JOURNAL OF FUZZY SYSTEMS, 2024, 26 (02) : 418 - 433
  • [47] Improved Results on Robust Stability Analysis and Stabilization for a Class of Uncertain Nonlinear Systems
    Belhaouane, Mohamed Moez
    Ghariani, Mohamed Faiez
    Ayadi, Hela Belkhiria
    Braiek, Naceur Benhadj
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2010, 2010
  • [48] Stability and stabilization of a class of switched nonlinear systems with time-varying delay
    Liu, Shilong
    Xiang, Zhengrong
    Chen, Qingwei
    APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (23) : 11534 - 11546
  • [49] Stability and stabilization of a class of nonlinear impulsive hybrid systems based on FSM with MDADT
    Department of Applied Mathematics, Xidian University, Xi'an 710071, China
    Nonlinear Anal. Hybrid Syst., (1-10):
  • [50] Stability and Stabilization of Fuzzy Event-Triggered Control for Positive Nonlinear Systems
    Ziguang Wang
    Aiwen Meng
    Hak-Keung Lam
    Bo Xiao
    Zhiquan Li
    International Journal of Fuzzy Systems, 2024, 26 : 418 - 433
12345