This study deals with the observer-based controller design problem for a class of networked control systems with multirate sampling. A matching mechanism is proposed to synchronise the sampled data between the plant and an observer, and computes the corresponding error. Using the error, the multirate observer is developed to estimate the state of the system in real time. A state feedback controller based on the observer is utilised to control the system. Different from discrete-time modelling methods, the resulting closed-loop system is modelled as a continuous-time system with multiple sawtooth inputdelays. Inspired by Wirtinger's inequality, a new Lyapunov-Krasovskii functional is constructed to analyse efficiently the closedloop system in the presence of time-varying network-induced delays. Then sufficient conditions for H∞ performance analysis and the observer-based controller design are presented. Finally, two illustrative examples show the effectiveness of the proposed method.