Further results on adaptive full-order and reduced-order observers for Lur’e differential inclusions

• An existence condition of the adaptive full-order observer for Lur’e systems is established.
• An existence condition of the adaptive reduced-order observer for Lur’e systems is given.
• Comparing with the existing results, the obtained conditions are easy to check by LMI.
• The assumptions on nonlinear perturbation functions are relaxed.

This paper is concerned with the adaptive observer design of Lur’e differential inclusions with unknown parameters. Under a relaxed assumption on nonlinear perturbation functions, a sufficient condition for the existence of an adaptive full-order observer is established. Comparing with results in the literature, the present conditions are complemented with a numerically reliable computational approach, which can be checked by means of linear matrix inequalities. Furthermore, it is shown that, under the sufficient condition, the existence of a reduced-order observer is guaranteed. Also, the reduced-order observer is designed. The effectiveness of the proposed design is illustrated via a simulation example.