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This study focuses on investigating the asymptotical stabilisability of time-delay switched systems with constrained switching signals and its applications in networked control systems (NCSs). First, based on an important lemma, asymptotical stabilisability criteria are established and stabilising switched output feedback controllers can be designed. Then, for NCSs with dropouts, the dropouts are modelled as the time delay in the control input and the switching signal in controller. Thus, the NCS with dropouts can be equivalently converted into a switched system with constrained switching signals and time delay. The asymptotical stabilisability criteria of such switched system can be applicable to the NCS with dropouts. The maximum allowable dropout bound can be obtained by solving an optimisation problem. Finally, two examples are given to illustrate the authors' main results.