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The stability analysis of network control systems still poses a challenge due to the nonlinear behavior induced by network transmissions. The current paper addresses the stability problem for a network control system which includes a nonlinear network transmission model. The network transmission model embeds the main characteristics of real TCP/IP network transmissions like time varying delays, packet loss and irregular situations. The closed-loop network control system is recasted as a switched linear system with multiple switching signals. The stability is investigated under arbitrary switching, by adopting a switched quadratic Lyapunov candidate function. Linear matrix inequality based conditions are derived for stability and controller design. Finally, an appropriate example illustrates how the approach is used.