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This paper considers network control systems (NCS) with time-delay. To deal with delay of NCS, both constant delay and time-varying delay cases are considered. In view of two classes of time-delay systems, based on the Lyapunov-Krasovskii functional, a new method of analyzing stability for time-delay systems is given by using golden section. Two asymptotically stable criterion using LMIs with less conservatism are derived. According to the criterion, the convex optimizations are established to design maximum allowable delay bound. An example shows that the performance of conservatism is improved.