Note on observer for lur´e differential inclusion systems

This note considers the reduced-order observer of Lur´e differential inclusion systems. The set-valued mappings in the differential inclusions are maximal monotone, but may not be compact and bounded. It is verified that if there exists a full-order observer, then there is also a reduced-order observer. The construction of the observer as well as the convergence and well-posedness of the observer are presented. An example is provided to illustrate the validation of the reduced-order observer.