Robust Multi-Objective Feedback Design by Quantifier Elimination

AbstractThis paper shows how certain robust multi-objective feedback design problems can be reduced to quantifier elimination (QE) problems. In particular it is shown how robust stabilization and robust frequency domain performance specifications can be reduced to systems of polynomial inequalities with suitable logic quantifiers, ∀ and ∃. Because of computational complexity the size of problems that can solved by QE methods is limited. However, the design problems considered here do not haveanalyticalsolutions, so that even the solution of modest-sized problems may be of practical interest