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Descriptor systems present a general mathematical framework for the modelling, simulation and control of complex dynamical systems arising in many areas of mechanical, electrical and chemical engineering. This paper presents a survey of the current theory of descriptor systems, concerning solvability, stability, model reduction, controllability, observability and optimal control.

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Descriptor Systems: A General Mathematical Framework for Modelling, Simulation and Control (Deskriptorsysteme: Ein allgemeines mathematisches Konzept für Modellierung, Simulation und Regelung)