Past, present, and future of quantifier elimination procedures in system theory

The role of quantifier elimination procedures in the tackling of multidimensional digital filter stability test based on the generalization of Sturm´s theorem appeared for the first time as a journal publication in 1974. That was followed in 1975 by a discursive documentation on the use of such methods to tackle output feedback stabilization and other control problems. Recent progress in software for symbol manipulations via serial as well as parallel processing encourage investigations into wider adoption of quantifier elimination theory based methods in problems involving higher number of free variables. This paper review the past and present status before giving future directions for research that incorporate the conflicting factors of accuracy of solution and computational cost for implementing for algorithms developed using particularly cylindrical algebraic decomposition