Observer design for differentiable Lipschitz nonlinear systems with time-varying parameters

This paper develops observer design techniques in a unified framework for both time invariant and parameter varying Lipschitz nonlinear systems that are differentiable w.r.t. state variables. First, a new sufficient condition for asymptotic convergence is developed for both the extended Luenberger observer and a two-DOF nonlinear observer for time-invariant nonlinear systems. In addition to ensuring asymptotic convergence, extension of this observer design technique to optimization of a L2 performance criterion is presented, which enables the observer to handle the unknown disturbance inputs as well as ensure robustness to model uncertainty. Next, augmentation of this technique to parameter varying nonlinear (PVNL) systems is developed. Different from methods suggested in the LPV literature, a simple but non-conservative finite dimensional relaxation method for quadratic parameter dependent LMIs is presented. These results constitute perhaps the first systematic observer design methodology in literature for PVNL systems. Finally, a simulation result for vehicle slip angle estimation is presented to verify the performance of the developed observer design methods.