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We investigate the observer-based switched control design problem for switched linear systems with time delay in detection of switching signal. First, an improved and generalised estimate on the matrix norm is established (Lemma 2 in Section 2). Then, based on two important lemmas, under the assumption that each subsystem is controllable and observable, online and offline observer-based switched control design methods to guarantee the asymptotical and exponential stabilisabilities are given, respectively. Finally, an example is given to illustrate the results. Our results complement the results of Xie et al. about state feedback stabilisation of switched linear systems.