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

页码：402 / 417

页数：16

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