Abstarct: DC-DC Quadratic Buck Converter (QBC) is a step down converter with a wider duty ratio in camparision with conventional buck converter and achieves to lower level voltage. Nonlinear and time variant structure of converter beside its nonminimum phase behaviour cause complexities to design controller. Controller aims include no ripples on output voltage, robustness against of uncertainties in parameters of converter and suitable speed in voltage regulation. µ synthesis controller by D-K iteration possesses high ability to satisfy control propuses but the main problem is high order controller that make difficulties in real time implementation. In this thesis a constraint optimization problem is solved by evolutionary algorithems to figure out to get a simple robust structure. In this approach, robust stability and robust performance baxsed on µ analysis are assumed as constraint and cost function of optimization so that coefficients of controller satisfy both robust stability and performance for closed loop system. Genetic algorithm, improved particle swarm optimization and artificial bee colonies are used to find a solution for this problem and in addition genetic algorithm has reached to best stability and performance in comparision with others. The maximum of structured singular values for stability and performance by evolutionary algorithms have lower value in comparision with D-K iteration. Acceptable performance of proposed controller is output voltage regulation in precence of uncertainties on parameters of system is illustrated by simulation results.