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In this paper, an observer-based stabilizing controller has been designed for networked systems involving both random measurement and actuation delays. The developed control algorithm is suitable for networked systems with any type of delays. By the simultaneous presence of binary random delays and making full use of the delay information in the measurement model and controller design, new and less conservative stabilization conditions for networked control systems are derived. The criterion is formulated in the form of a nonconvex matrix inequality of which a feasible solution can be obtained by solving a minimization problem in terms of linear matrix inequalities. An illustrative example is presented to show the applicability of the proposed design technique.