Ellipsoid-Based Interval Estimation for Lipschitz Nonlinear Systems

This article proposes an intervalestimation method for discrete-time Lipschitz nonlinear systems via observer design and ellipsoidal analysis. A robust observer with novel structure is presented, which provides more degrees of design freedom and can be applied to enhance the interval estimation performance. To handle the nonlinear term in Lipschitz systems, we use the reformulated Lipschitz property to transform the nonlinear error dynamics into a linear parameter-varying form. After the transformation, the robustness performance of the proposed observer is characterized with the aid of peak-to-peak index. Furthermore, the comprehensive interval estimation results are obtained by using the peak-to-peak performance and the ellipsoidal analysis. Numerical simulation results are conducted to demonstrate the viability and validity of the presented method.