Gridding-based H_∞ observer design for the Lorenz 63 system using an NLPV reformulation
Abstract
T his paper presents a robust H_ ∞ observer design for the Lorenz 63 system based on a Nonlinear Parameter-Varying (NLPV) reformulation. The nonlinear dynamics are approximated by gridding the state space and constructing local linear models. At each grid point, an observer gain is synthesized by solving a linear matrix inequality (LMI), with a common Lyapunov function ensuring stability across the operating range. The observer gain is updated online via barycentric interpolation using the current estimated state. The approach enables real-time state estimation with guaranteed stability and disturbance attenuation. Simulation results under both noisy and noise-free conditions, and a comparison with an Extended Kalman Filter (EKF), confirm the effectiveness of the proposed design. Quantitative evaluations using Root Mean Square Error (RMSE), Normalized RMSE (NRMSE), and the coefficient of determination R 2 demonstrate high estimation accuracy and robustness of the observer across a range of dynamic behaviors in the Lorenz 63 system.