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This study deals with the β-exponential stability and stabilisation problems for a class of T-S model-based neutral systems. To solve these problems, new LyapunovβKrasovskii functional candidates for this class of systems can be chosen by using the delay-decomposition approach and introducing some exponential functions into corresponding integrands. β-exponential stability conditions of the TβS model-based neutral systems are established by using the LyapunovβKrasovskii functional and a modification integral inequality. An LMI-based state feedback controller design strategy for this class of systems is proposed based on one of the β-exponential stability conditions. Two numerical examples are also provided to illustrate the effectiveness of the proposed approach.