Design of an H_∞ observer for nonlinear parameter-varying systems with lipschitz nonlinearity and model uncertainty

This paper presents the design of an H_∞ observer for a class of Nonlinear Parameter-Varying (NLPV) systems featuring Lipschitz-continuous nonlinearities, bounded model uncertainties, and external disturbances. The proposed observer ensures robust state estimation while satisfying prescribed performance criteria. A Lyapunov-based approach is adopted, utilizing a polytopic representation to capture the dependence of the system matrices on the scheduling parameters. Sufficient conditions for the existence of the observer are expressed in terms of Linear Matrix Inequalities (LMIs), which are evaluated at the vertices of the polytope. The observer gain matrices are obtained by solving these LMIs, thereby guaranteeing robustness against model uncertainties and external disturbances across the entire operating range. The effectiveness and robustness of the proposed observer design are demonstrated through a simulation study involving a 2-DOF robotic manipulator.