A bridge between robust control and computational algebra

For multi-objective design and robust control synthesis problems, the methods based on Quantifier Elimination (QE) have been proposed. QE based methods are really suitable for such problems but, in general, they have a drawback on computational complexity. In this chapter, we will propose an efficient symbolic method for a parameter space approach based on sign definite condition (SDC) by a special quantifier elimination using Sturm–Habicht sequence. Then we examine its feasibility, in particular, for multi-objective control using low degree fixed-structure controller by showing the several experimental results.