On differential-algebraic control systems

In this dissertation we study differential-algebraic equations (DAEs) of the form Ex'=Ax+f. One aim of the thesis is to derive the quasi-Kronecker form (QKF), which decomposes the DAE into four parts: the ODE part, nilpotent part, underdetermined part and overdetermined part. Each part describes a different solution behavior. The QKF is exploited to study the different controllability and stabilizability concepts for DAEs with f=Bu, where u is the input of the system. Feedback decompositions, behavioral control and stabilization are investigated. For DAE systems with output equation y=Cx, we may define the concept of zero dynamics, which are those dynamics that are not visible at the output. For right-invertible systems with autonomous zero dynamics a decomposition is derived, which decouples the zero dynamics of the system and allows for high-gain and funnel control. It is shown, that the funnel controller achieves tracking of a reference trajectory by the output signal with prescribed transient behavior. Finally, the funnel controller is applied to the class of MNA models of passive electrical circuits with asymptotically stable invariant zeros.