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A2: Analysis and computation of stability exponents for delay differential-algebraic equations
Prof. Dr. Volker Mehrmann 
Delay differential-algebraic equations (DDAEs) arise in a variety
of applications including flow control,
biological systems and electronic networks. We will study existence and uniqueness as well as the
development of numerical methods for general nonlinear DDAEs. For this, regularization techniques
need to be performed that prepare the DDAE for numerical simulation and control. We will derive
such techniques for DDAEs on the basis of a combination of time-differentiations and time-shifts, in
particular for systems with multiple delays. We also plan to extend the spectral stability theory, i.e. the
concepts of Lyapunov, Bohl and Sacker-Sell spectra, to DDAEs. We will also develop numerical methods
for the computation of these spectra using semi-explicit integration methods. Another goal is to study
the solution of algebraically constrained partial delay-differential equations arising in flow control and to
derive discretization as well as optimal control methods in space and time.