Incremental input-to-state stability for Lur'e systems and asymptotic behaviour in the presence of Stepanov almost periodic forcing

Abstract

We prove (integral) input-to-state stability results for a class of forced Lur'e differential inclusions and use them to investigate incremental (integral) input-to-state stability properties of Lur'e differential equations. The latter provide a basis for the derivation of convergence results for trajectories of Lur'e equations generated by Stepanov almost periodic inputs.