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A new discretization framework for input/output maps and its application to flow control

Heiland, Jan; Mehrmann, Volker; Schmidt, Michael

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

We discuss the direct discretization of the input/output map of linear time-invariant systems with distributed inputs and outputs. At first, the input and output signals are discretized in space and time, resulting in a matrix representation of an approximated input/output map. Then the system dynamics is approximated, in order to calculate the matrix representation numerically. The discretization framework, corresponding error estimates, a SVD-based system reduction method and a numerical application in optimization problems are presented, and illustrated for a heat control and a flow control system.