Unknown input dynamic observer for a class of nonlinear systems using contraction analysis

This paper proposes a novel methodology to design an unknown-input dynamic observer for a class of nonlinear systems, grounded in contraction theory. The primary contributions include a contraction-based framework for handling unknown inputs and the development of a dynamic observer structure that enhances robustness and steady-state accuracy. Existence and stability conditions are established using contraction analysis, ensuring exponential convergence of the estimation error. These conditions are further expressed as simplified linear matrix inequalities (LMIs), enabling computationally efficient implementation despite system nonlinearities. The proposed observer is evaluated against existing methods through numerical simulations, demonstrating improved performance and practical applicability in the presence of different unknown input.