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. The worst-case two-impact disturbance is compared with the worst-case rectangular pulse disturbance in terms of the value of the performance index; 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.