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This technical note deals with continuous-time switched linear systems and addresses the problem of characterizing open-loop switching strategies, based on dwell time specifications, assuring a pre-specified root mean square gain (RMS). As a natural consequence of treating general systems of this particular class in terms of order and number of subsystems, only sufficient conditions are worked out. However, as positive features, they are expressed through linear matrix inequalities (LMI) being thus numerically solvable in polynomial time and allow the treatment of stable switched linear systems which do not admit a common Lyapunov function. The conservativeness of the proposed design method is evaluated by comparison with other results available in the literature by means of two simple illustrative examples.