In recent studies, Asai proposed a strategy to analyze disturbance response of control systems across switching. It was shown that the performance deterioration caused by the disturbance can be assessed quantitatively by a sort of <i>L</i><sub>2</sub> gain of the control system, which can be regarded as a generalization of the well-studied Hankel norm of linear time-invariant systems. In addition, explicit formulas to compute the <i>L</i><sub>2</sub> gain have also been derived. The derivation explored there is, however, rather involved and does not conform to the elegant results already known in the analysis of Hankel operators. Motivated by these facts, in the present note, we give a concise proof for the results by Asai based on linear operator representations. It turns out that the results can readily be obtained by describing a procedure to compute the norm of the associated compact linear operator.