A Second-Order Observer Based on Dissipativity and Homogeneity Properties for Uncertain Nonlinear Systems

In this paper, we propose a global second-order dissipative homogeneous observer (DH-observer) that can estimate the states of an uncertain nonlinear system with unknown inputs in finite time. The system must be strongly observable with respect to unknown inputs (UIs), uniformly in the known input. To handle the UIs and non-Lipschitz nonlinearities, the proposed observer combines dissipative and homogeneous properties. The convergence of the DH-observer to the system states is proven through a Lyapunov function. Finally, to showcase the effectiveness of the proposed method, the paper includes an academic example.