Robustness of exponential stability to singular perturbations and delays

被引：15

作者：

Grammel, G. ^{[1
]}

机构：

[1] Tech Univ Munich, Ctr Math, D-85747 Garching, Germany

来源：

SYSTEMS & CONTROL LETTERS | 2008年 / 57卷 / 06期

关键词：

averaging; singular perturbation; delay; exponential stability;

D O I：

10.1016/j.sysconle.2007.11.009

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Singularly perturbed nonlinear differential equations with small time delays in the slow variables are considered. Averages of the fast variables are used in order to obtain a sufficient condition under which the exponential stability of the slow subsystem is robust to singular perturbations and delays. (C) 2007 Elsevier B.V. All rights reserved.

引用

页码：505 / 510

页数：6

共 22 条

[1] On exponential stability of nonlinear time-varying differential equations [J].

Aeyels, D ;

Peuteman, J .

AUTOMATICA, 1999, 35 (06) :1091-1100

[2]

[Anonymous], GLAS MATH

[3] Singularly perturbed ordinary differential equations with dynamic limits [J].

Artstein, Z ;

Vigodner, A .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1996, 126 :541-569

[4] Stability in the presence of singular perturbations [J].

Artstein, Z .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1998, 34 (06) :817-827

[5] On singularly perturbed retarded functional differential equations [J].

Artstein, Z ;

Slemrod, M .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2001, 171 (01) :88-109

[6] ON THE EXPONENTIAL STABILITY OF SINGULARLY PERTURBED SYSTEMS [J].

CORLESS, M ;

GLIELMO, L .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1992, 30 (06) :1338-1360

[7] On a representation of the limit occupational measures set of a control system with applications to singularly perturbed control systems [J].

Gaitsgory, V .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2004, 43 (01) :325-340

[8] Exponential stability of nonlinear differential equations in the presence of perturbations or delays [J].

Grammel, G. ;

Maizurna, I. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2007, 12 (06) :869-875

[9] Exponential stability of nonlinear singularly perturbed differential equations [J].

Grammel, G .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2005, 44 (05) :1712-1724

[10] On the relevance of resonances [J].

Grammel, G .

NONLINEARITY, 2005, 18 (03) :1121-1140

← 1 2 3 →