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This study investigates the problem of model predictive control (MPC) for networked multirate control systems (NMCSs) with the output sampling period several times larger than the input updating period. Both sensor-to-controller and controller-to-actuator network-induced delays are considered and are assumed to be upperbounded by one output sampling period. Firstly, using a modified multirate MPC scheme, where the future control sequence is used to compensate for the network-induced time delays, the closed-loop NMCSs are described as switched systems. Sufficient stability conditions are established via a switched Lyapunov function approach. Then, a controller design method for stabilising NMCSs is proposed based on a finite input and state horizon cost with a finite terminal weighting matrix. The feedback gain matrix dependent of every sampling output can be obtained by solving linear matrix inequalities (LMIs). Finally, examples are provided to show the effectiveness of the proposed method.