Preprint 35-2012

Robust stability of differential-algebraic equations

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