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This study is concerned with the stability analysis and stabilisation problem of the full-envelope networked flight control systems, where the system dynamic can be modelled as the switched time-varying delay systems evolving on the locally overlapped switching law. Firstly, a stability analysis tool based on the common Lyapunov function method and the average dwell time method is proposed to guarantee the exponential stability of the considered system. The common Lyapunov-Krasovskii function is utilised to obtain delay-dependent criterion and guarantee exponential stability for each locally overlapped group of the switched time-varying delay system, and the average dwell time approach is used to guarantee stability when switching occurs between different locally overlapped groups. Then, a control design algorithm is provided for determining the state feedback controller gain in the linear matrix inequality formalism, which makes it easier to obtain the gain by using existing tools. Finally, the illustrative example of the stability analysis and the flight controller design for the highly manoeuvrable technology vehicle are given, and it demonstrates the effectiveness of the proposed results.