On the L2-gain of a double integrator with feedback loop saturation nonlinearity

We consider the open problem of whether there exists finite L/sub 2/ gain in each channel of a double integrator in feedback interconnection with a saturation nonlinearity. It has been shown by Liu-Chitour-Sontag (1996) that the L/sub 2/ gain from input to the output of the first integrator is infinite. In this paper, by constructing a special excitation, we show that the L/sub 2/ gain from input to the output of the second integrator is also infinite.