AParameter Space Approach for Fixed-0rder robust controller synthesis by symbolic computation

In this paper we present anew parameter space design method for robust control synthesis, in particular in terms of real stability radius, using quantifier elimination (QE). We also aim at practicality by employing the scheme to combine sign definition condition (SDC) and special QE algorithm using Sturm-Habicht sequence. We show some concrete examples demonstrating the validity of our approach. 1Introduction For robust control synthesis and multi-0bjective design, aparameter space approach is known to be one of the effective methods. The parameter space approach can be utilized to determine the set of certain parameters which satisfies the given specifications in aparameter space. Recently, the parameter space design accomplished by using quantifier elimination (QE) has been proposed for robust multi-0bjective design problems $[4, 6] $ : The robust control problems are reduced to first-0rder formula descriptions, then can be solved by applying general $\mathrm{Q}\mathrm{E} $. However, naive reduction of the control problems to the QE problems, in general, complicated to achieve QE computation efficiently. This is aserious issue in view of efficiency because the worst-case complexity of general QE algorithm based on cylindrical algebraic decomposition (CAD) algorithm has doubly exponential behavior