Linear programming approach to robust controller design by a quantifier elimination

In this paper we present a systematic method to obtain all feasible relaxations of a given design specification for robust controller synthesis problems by using quantifier elimination (QE) and, in particular, we apply it to robust pole assignment problems. Our method consists of the problem reduction to an LP problem and usage of a suitable special QE algorithm based on virtual substitution. The validity of the approach is demonstrated by some concrete computational examples.