Design of a Nonlinear Observer for a Class of Locally Lipschitz Systems by Using Input-to-State Stability: An LMI Approach

This note addresses the problem of state estimation for a class of local Lipschitz nonlinear systems under the effect of noise/disturbances. An observer structure based on Hilbert projection is used to handle the same class of nonlinearities. The boundedness of the state estimation error of the proposed observer is guaranteed by deploying the input-tostate stability (ISS) property. Based on ISS stability criterion, the new LMI condition is derived by combining a well-known LPV approach with a variant of Young inequality and novel matrix multipliers. The proposed LMIs have more decision variables than the methodologies presented in the literature, which provides extra degrees of freedom, and hence enhances LMI feasibility. Further, the effectiveness of the developed approach is highlighted through a numerical example. The performance of the observer is validated through the application of slip angle estimation in a nonlinear autonomous vehicle.