Numerical methods in control, from pole assignment via linear quadratic to H infinity control

We study classical control problems like pole assignment, stabilization, linear quadratic control and H1 control from a numerical analysis point of view. We present several examples that show the difficulties with classical approaches and suggest reformulations of the problems in a more general framework. We also discuss some new algorithmic approaches. AMS subject classification. 65F15, 93B40, 93B36, 93C60. Authors: Volker Mehrmann and Hongguo Xu Fakultat fur Mathematik, TU Chemnitz, D-09107 Chemnitz, FRG. Supported by Deutsche Forschungsgemeinschaft, within Sonderforschungsbereich SFB393, `Numerische Simulation auf massiv parallelen Rechnern'. 1 Introduction In the last 40 years linear systems theory (control theory) has evolved into a mature field that has found a stable position on the borderline between applied mathematics, engineering and computer science. The major success is not only due to the fact that beautiful mathematical theories (like linear algebra, ring theory, rep..