BIBO stability integral ( L∞-gain) for second-order systems with numerator dynamics

Abstract

It is shown that the most stressful bounded disturbance for linear stable second-order systems with numerator dynamics is bang–bang and can be realized in feedback form using a switch curve. Especially for the second-order systems with a finite zero, an explicit formula is given for the bounded input–bounded output stability integral based on the time maximum disturbance switch curve. This closed analytic form requires less-computational effort and gives an intuitive feeling as to how the L ∞-gain will change with the free system parameters.