Observer design for Lur'e systems with monotone multivalued mappings

in this paper we present a constructive observer design procedure for a class of nonsmooth dynamical systems, namely systems of Lur'e type with a monotone multivalued mapping in the feedback path. Examples of such systems include various classes of hybrid systems. Under the assumption that the observed system is well behaved, we prove that the proposed observers are well-posed (i.e. that there exists a unique weak solution to the observer dynamics), and that the observer asymptotically recovers the state of the observed system, under the assumption that the weak solutions of the observer are absolutely continuous. The results are illustrated on an example of a deep sea oil drilling assembly with a string.