Comparison of the responses of a nonlinear oscillator to the worst-case disturbance consisting of two instantaneous impacts and the worst-case rectangular pulse disturbance

An oscillator with quadratic-law damping subjected to two successive instantaneous impacts is considered; the impacts have the same directions and their total impulse is given. The worst-case disturbance that maximizes the peak absolute value of the displacement of the oscillator’s body from the equilibrium position (taken as a performance index) is sought. The parameters of the two-impact disturbance that provides a maximum for the performance index are determined. A comparison of the worst-case two-impact disturbance with the worst-case rectangular pulse disturbance in terms of the value of the performance index is performed; both disturbances have the same impulse. It is shown that the worst-case rectangular pulse provides a larger value for the peak absolute value of the displacement of the oscillator than the two-impact disturbance does.