Network Control Systems (NCS) arise in many real-world applications and they have been an active area over recent decades. Using NCSs instead of traditional controllers has led to significant decrease in costs, weight and power of installations, also increase in reliability of control systems. Despite these advantages, NCSs confront various challenges, such as time varying delays and data packet dropouts in control data transfer which leads to instability. In this paper, the stability analysis and stabilizing with state feedback are studied for NCSs which includes time varying delays in state equations. This goal is achieved by introducing a new functional and using the Lyapunov-Krasovskii approach. Then, an accurate estimation of derivative of functional is obtained by applying Wirtinger and Reciprocally convex combination inequalities. In the proposed method, a stability criterion is derived with less conservatism and complexity. Afterwards, the problem of controller design is examined in which the state feedback controller is designed based on stability criterion. Finally, the dynamic model of the satellite as an examples is used to demonstrate the advantages of proposed method which illustrates our proposed method has desirable influence in decreasing conservatism of results and leading to better performance.