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.