On the stabilizability of near‐grazing dynamics in impact oscillators

Abstract

AbstractA constructive proof is presented for the existence of event‐driven control strategies that guarantee the local persistence of system attractors with at most low‐velocity contact in vibro‐impacting oscillators. In particular, sufficient conditions are formulated on the linearization of the control strategies along a grazing periodic trajectory, i.e. an oscillating motion that achieves zero‐relative‐velocity contact with a mechanical obstacle, to ensure the asymptotic stability of the grazing trajectory and, consequently, sustained dynamics in the vicinity of the grazing trajectory even under small changes in system parameters. The implications of the methodology are illustrated with linear and nonlinear, single‐ and multiple‐degree‐of‐freedom examples of vibro‐impact oscillators. Copyright © 2007 John Wiley & Sons, Ltd.