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This paper discusses the Hinfin control synthesis for discrete-time linear networked systems with time-varying delays in input and output channels. The time-varying delays are assumed to take their values in finite sets, and assumed to be measurable only on line. Our formulation allows the (worst) case of random delays with no stochastic assumption. Considering delays as parameters, we first reformulate the Hinfin control problem for networked systems with time-varying delays into that for linear parameter-varying (LPV) systems with jumping parameters. Next, we present a sufficient condition, which is given as a finite set of linear matrix inequalities (LMIs) depending on values of parameters, for synthesizing a gain scheduled output feedback control for LPV systems with jumping parameters, and based on this condition, derive an output feedback controller scheduled with input-output delays. Finally, applying our controller to the networked system composed of the cart and inverted pendulum plant and the input-output channels with random jumping delays, we show that our controller, which does not assume any stochastic property on delays, displays a good performance almost similar to that of the existing stochastic Hinfin controller.