The four-parameter lag-lead compensator design has received much attention in the last two decades.However,most approaches have been either trial-and-error or only for special cases.This paper presents a non-trial-and-error design method for four-parameter lag-lead compensators.Here,the compensator design problem is formulated into a polynomial function optimization problem and solved by using the recently developed sum-of-squaras (SOS) techniques.This result not only provides a useful design method but also shows the power of the SOS techniques.