On solving semidefinite programming by quantifier elimination

Abstract

Several interesting control system design and analysis problems can be reduced to quantifier elimination (QE) problems. In this paper, we focus on semidefinite programming (SDP) problems, which are one of the generic linear matrix inequality (LMI) problems. We present a new symbolic method based on QE for the SDP problems and show some experiment by using existing QE package to demonstrate the capability of the method. Though currently this method is practically applicable to modest size problems which existing QE software can solve, it gives one exact solutions and enables one to deal with nonconvex as well as parametric cases. Moreover, in our scheme, the model or parameter uncertainties are easy to incorporate in the SDP problems.