On stability of time-varying linear differential-algebraic equations

被引：21

作者：

Berger, Thomas ^{[1
]}

Ilchmann, Achim ^{[1
]}

机构：

[1] Ilmenau Univ Technol, Inst Math, D-98693 Ilmenau, Germany

来源：

INTERNATIONAL JOURNAL OF CONTROL | 2013年 / 86卷 / 06期

关键词：

time-varying linear differential algebraic equations; exponential stability; Lyapunov's direct method; Lyapunov equation; Lyapunov function; standard canonical form; STATED LEADING TERM; PRESERVING INTEGRATION; BEHAVIORAL-APPROACH; CANONICAL FORM; SYSTEMS; RADII; BOHL;

D O I：

10.1080/00207179.2013.773087

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We develop a stability theory for time-varying linear differential algebraic equations (DAEs). Well-known stability concepts of ordinary differential equations are generalised to DAEs and characterised. Lyapunov's direct method is derived as well as the converse of the stability theorems. Stronger results are achieved for DAEs, which are transferable into standard canonical form; in this case the existence of the generalised transition matrix is exploited.

引用

页码：1060 / 1076

页数：17

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