This paper is concerned with the dynamic output feedback control issue for a class of networked control systems with medium access constraints, network-induced delays and packet dropouts. It is assumed that the medium access constraints at both sides of the controller obey the Markov distribution, the upper bound of the network-induced delays is less than one sampling period, and the packet dropouts of networked channels can be described by i.i.d Bernoulli distribution processes. Then, the networked control systems are modelled as a class of asynchronous dynamic systems. According to Lyapunov stability theory and switching system theory, the dynamic output feedback controller is designed to guarantee the exponential stability of networked systems with the given decay rate. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.