Abstract-This paper proposes a new scheduling method to obtain a maximum allowable delay bound for a scheduling of networked discrete control systems. The proposed method is formulated in terms of linear matrix inequalities (LMI) and can give a much less conservative delay bound than the existing methods. An event based network scheduling method is presented based on the delay bound obtained through the proposed method, and it can adjust the sampling period to allocate identical utilization to each control loop. The presented method can handle sporadic emergency data, periodic data, and non-real-time data.