Proposes a mathematical formulation of bumpy responses and a method to analyze their magnitudes. Bumpy responses often appear when switching occurs in control systems. Since those responses are harmful, several methods have been proposed to attain bumpless transfer. However, most of the existing methods do not provide any guarantee for the resultant performance nor deal with uncertainty explicitly. This paper formulates the magnitude of bumpy responses as the worst-case /spl Lscr//sub 2/ gain from past disturbance to future outputs and proposes a method to analyze the worst-case gain based on linear matrix inequalities. Numerical examples clarify the effectiveness of the proposed method.