Applications of Quantifier Elimination Theory to Control Theory

In this paper we show how a number of interesting linear control system analysis and design problems can be reduced to Quantifier Elimination (QE) problems. We assume a fixed structure for the compensator, with design parameters qi. The problems considered are problems that currently have no general solution, e.g. the output stabilization problem, the simultaneous stabilization problem, the robust multiobjective problem, etc. However, the problems must be of modest complexity if existing QE software packages are to produce answers. The software package QEPCAD is used to solve some numerical design examples