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

It is shown that the most stressful bounded disturbance for linear stable s econd-order systems with numerator dynamics is bang-bang and can be realize d in feedback form using a switch curve. Especially for the second-order sy stems with a finite zero, an explicit formula is given for the bounded inpu t-bounded output stability integral based on the time maximum disturbance s witch curve. This closed analytic form requires less-computational effort a nd gives an intuitive feeling as to how the L-infinity-gain will change wit h the free system parameters. (C) 2000 Elsevier Science Ltd. All rights res erved.