Convergence based synchronization of unilaterally constrained multibody systems

The convergence property of a dynamical system is a strong condition with various useful implications. A convergent system exhibits a bounded globally attractively stable solution and thus its asymptotic (or symptotic) behaviour is independent of initial conditions. This paper presents conditions for the convergence property of mechanical systems submitted to unilateral constraints. A key role plays the maximal monotonicity of the impact law, which is a stronger condition than dissipativity. The convergence property can directly be used for the design of a state observer for mechanical systems with unilateral constraints. These observers are based on master-slave synchronization and replicate the full state of the observed system for every choice of initial conditions using only the impact time instants. The results are illustrated with the example of a harmonically excited beam with unilateral support.