Dissipative design of adaptive observers for systems with multivalued nonlinearities

An adaptive observer for a class of systems with discontinuous or multivalued nonlinearities is developed. The design is based on the combination of an adaptive observer form and the dissipative observer design for multivalued systems, introduced previously in the literature. An extension of this result is also obtained by showing that if the relative degree of the adaptive observer form is incremented by one, the design of the adaptive observer is still possible.