Adaptive full-order and reduced-order observers for the Lur’e differential inclusion system

This paper deals with the observer design for the Lur’e differential inclusion system with unknown parameters. The set-valued mapping in the differential inclusion is upper semi-continuous, closed, convex, bounded and monotone. First, under some assumptions an adaptive full-order observer is designed for the system. Then, under the same assumptions, a reduced-order observer is proved to exist. An example is provided to show the validation of the designed observers.