Differentially Positive Systems

被引：58

作者：

Forni, Fulvio ^{[1
,2
]}

Sepulchre, Rodolphe ^{[1
,2
]}

机构：

[1] Univ Cambridge, Dept Engn, Cambridge CB2 1PZ, England

[2] Univ Liege, Dept Elect Engn & Comp Sci, B-4000 Liege, Belgium

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2016年 / 61卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

Convergence; differentially positive systems; MONOTONE SYSTEMS; STABILITY; CONTRACTION; EXCITABILITY; OSCILLATIONS; CONVERGENCE; EQUILIBRIA; CONSENSUS; SIGN;

D O I：

10.1109/TAC.2015.2437523

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The paper introduces and studies differentially positive systems, that is, systems whose linearization along an arbitrary trajectory is positive. A generalization of Perron-Frobenius theory is developed in this differential framework to show that the property induces a conal order that strongly constrains the asymptotic behavior of solutions. The results illustrate that behaviors constrained by local order properties extend beyond the well-studied class of linear positive systems and monotone systems, which both require a constant cone field and a linear state space.

引用

页码：346 / 359

页数：14

共 49 条

[1]

Absil PA, 2008, OPTIMIZATION ALGORITHMS ON MATRIX MANIFOLDS, P1

[2]

Aliluiko A.M., 2006, Ukrainian Mathematical Journal, V58, P1635

[3]

Angeli D, 2004, LECT NOTES CONTR INF, V301, P135

[4] Multi-stability in monotone input/output systems [J].

Angeli, D ;

Sontag, ED .

SYSTEMS & CONTROL LETTERS, 2004, 51 (3-4) :185-202

[5] Monotone control systems [J].

Angeli, D ;

Sontag, ED .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2003, 48 (10) :1684-1698

[6] Translation-invariant monotone systems, and a global convergence result for enzymatic futile cycles [J].

Angeli, David ;

Sontag, Eduardo D. .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2008, 9 (01) :128-140

[7]

Angeli D, 2012, IEEE DECIS CONTR P, P2989, DOI 10.1109/CDC.2012.6426795

[8]

[Anonymous], 1971, LOCALLY CONVEX TOPOL

[9]

[Anonymous], 2013, Mathematical control theory: deterministic finite dimensional systems

[10]

[Anonymous], 1994, Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, DOI 9780738204536

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