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It has become a common practice to employ networks in control systems for connecting controllers and sensors/actuators on controlled plants and processes. A networked switched control system, as a special case of networked control systems, is studied. Such a system with packet dropout is represented as an asynchronous dynamical switched system. Both the switched control system state dropout and the switching signal dropout are considered in the system dynamics simultaneously. Sufficient conditions for the exponential stability and control synthesis of networked switched control systems at a fixed known data packet transmission rate under arbitrary switching sequences are derived. Switched Lyapunov-Krasovskii technique is used in analyzing the stability of the system accordingly reduces the conservativeness of using common Lyapunov functions. Finally, a lower bound on packet transmission rate that guarantees the stability of networked switched control systems is discussed.