A synchronization‐based state observer for impact oscillators using only collision time information

Summary We present the design of a state observer for Lagrangian systems subjected to frictionless geometric unilateral constraints. A master–slave synchronization setup is used in which the unidirectional coupling only consists of the information of the impact time instants. After a brief synchronization phase, the obtained observer replicates the full state of the observed system, independently of the initial conditions and even in the presence of accumulation points (Zeno behavior). The key idea is that the (virtual) observer system is subjected to switched kinematic unilateral constraints such that it may enjoy the property of incremental stability when the impact law is maximal monotone. The main inequality impact laws for hard unilateral constraints, that is, the generalized Poisson's and Newton's impact law, are under mild assumptions maximal monotone, which is a stronger condition than dissipativity. The results are applied to two different examples of mechanical impact oscillators. Copyright © 2015 John Wiley & Sons, Ltd.