This paper is devoted to the stability analysis and sampled-data controller design problem for networked control systems subject to network-induced delays. The objective is to provide relaxed conditions in terms of linear matrix inequalities. Indeed, reducing the conservatism of such conditions allows to maximize the admissible range of the network-induced delays. To do so, an augmented Lyapunov–Krasovskii functional is proposed, which involves a novel augmented state vector to include as much as possible the information from the time-varying network-induced delay into the stability conditions, together with the use of extended Wirtinger-based inequalities, an extended reciprocal convexity approach and the Finsler’s lemma. Then, declined from the proposed stability conditions, new relaxed delay-dependent conditions for the design of networked sampled-data controllers are proposed. These allow to obtain simultaneously the controller gains and the maximal allowable bound of the network-induced delays with regards to its lower bound. Three illustrative examples are provided to show the effectiveness of the proposed networked control systems stability and controller design conditions, as well as to highlight the so raised conservatism improvements regarding the previous relevant results from the literature.