Abstract: To further strengthen the robust control of Lurie system，based on the early theoretical study，a controller design theory for Lurie systems with time-varying delay uncertainty is discussed with the application of the new cross-term definition method． By constructing a new Lyapunov functional and following the characteristics of Lurie system，the new feedback controllers are designed for singularly perturbed Lurie systems with uncertain time-varying delay in the sector region ［V1，V2］，and the state feedback control laws of time-delay dependent and time-delay independent are deduced． Finally，the feasibility and effectiveness are illustrated by the correspanding numerical example．

Key words: lurie systems, strongly absolute stability, state feedback control law, cross terms defined method, delay-dependent, delay-independent, lyapunov-krasovskii functional ( L-K ) , linear matrix inequality ( LMI)