TY - GEN A1 - Benner, Peter A1 - Losse, Philip A1 - Mehrmann, Volker A1 - Voigt, Matthias T1 - Numerical Linear Algebra Methods for Linear Differential-Algebraic Equations N2 - A survey of methods from numerical linear algebra for linear constant coefficient differential-algebraic equations (DAEs) and descriptor control systems is presented. We discuss numerical methods to check the solvability properties of DAEs as well as index reduction and regularization techniques. For descriptor systems we discuss controllability and observability properties and how these can be checked numerically. These methods are based on staircase forms and derivative arrays, transformed with real orthogonal transformations that are discussed in detail. Then we use the reformulated problems in several control applications for differential-algebraic equations ranging from regular and singular linear-quadratic optimal and robust control to dissipativity checking. We discuss these applications and give a systematic overview over the theory and the numerical solution methods. In particular, we show that all these applications can be treated with a common approach that is based on the computation of eigenvalues and deflating subspaces of even matrix pencils. The unified approach allows to generalize and improve several techniques that are currently in use in systems and control. KW - descriptor system KW - differential-algebraic equation KW - linear-quadratic optimal control KW - $\mathcal{H}_\infty$ control KW - dissipativity KW - even matrix pencil Y1 - 2014 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1331 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-13318 ER -