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On Generalised Eigenvalue Problems Arising In Systems and Control Theory

System and control theory has long been a rich source of problems for the numerical linear algebra community. In some problems, conditions on analytic functions of a complex variable are usually evaluated by solving a special generalized eigenvalue problem. Our principal contribution in this paper is to demonstrate that many of these problems can be solved, in a very straightforward manner, not by resorting to generalized eigenvalue solvers, but by solving standard eigenvalue problems. We also give a number of new characterizations of well known concepts such as strict positive realness.