A note on adaptive observer for the Lur’e differential inclusion system

This paper considers the adaptive observer design problem for the Lur’e differential inclusion system with unknown parameters. Different from the current work, the proposed observer does not hold any set-valued mapping and the uncertain parameters can also be identified. Firstly, the adaptive observer is designed for the Lur’e differential inclusion system, and it is proved to be valid by Lyapunov stability theory. Then, based on the canonical form of the system matrix, the sufficient and necessary condition for one assumption is presented in both SISO and MIMO cases. Finally, numerical examples are simulated to show the effectiveness of the proposed method.

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