Author(s) :
Nguyen Huu Du
,
Vu Hoang Linh
,
Volker Mehrmann
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 35-2012
MSC 2000
- 93B35 Sensitivity
-
93D09 Robust stability
Abstract :
This paper presents a survey of recent results on the robust stability analysis
and the distance to instability for linear time-invariant and time-varying differential-algebraic equations (DAEs).
Different stability concepts such as exponential and asymptotic stability are studied and their robustness
is analyzed under general as well as restricted sets of real or complex
perturbations. Formulas for the distances are presented whenever these are available and the continuity of the distances in terms of the data is discussed. Some open problems and challenges are indicated.
Keywords :
differential-algebraic equation, robust stability, stability radius, spectrum, spectral set, restricted perturbation