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In this brief article, the stability and disturbance attenuation property in the sense of ℓ2 gain for switched linear discrete-time systems are investigated. The computation of ℓ2 gains against dwell time has been viewed as an open problem so far. A novel dwell-time dependent Lyapunov function (DTDLF) is introduced to study the stability and ℓ2 gain analysis problems. The main advantage of DTDLF approach is that the derived conditions are all convex in system matrices, thus it is capable to be generalised to switched systems with uncertainties. Then, as an application, the ℋ∞ control problem is considered. Based on the DTDLF approach, the control synthesis procedures including state-feedback controllers and switching law design are unified into one-step method that explicitly facilitates the control synthesis process. Finally, numerical examples are provided to illustrate the proposed results.