Abstract: Design of state-feedback guaranteed cost controllers is considered for a class of norm bounded uncertain singular systems and a time-multiplied linear quadratic cost function.Such a cost function enables the state res-ponses to approach zero more quickly,and shortens stabilizing time of the systems.The sufficient and necessary condition and the optimal design method of guaranteed cost controllers based on bilinear matrix inequalities(BMIs),quadratic matrix inequalities(QMIs) and LMI are obtained.The numerical example shows the validity of our conclusion via the softwares of SDP and BMI.