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The saturation input control problem of discrete-time networked systems via adaptive event-triggered communication scheme is discussed in this paper. The criteria are derived by utilising a new Lyapunov functional to guarantee that the considered networked system with randomly occurring infinite distributed delays, random packet losses and sensor saturation is exponentially stable in mean square sense. A novel adaptive event-triggered law is proposed, which is dependent on the exponentially stable index α. The effectiveness of our proposed method is illustrated by both theoretical analysis and numerical simulations. [ABSTRACT FROM AUTHOR]