Low peaking-phenomenon cascade high-gain observer design with LPV/LMI method

To cope with the well-known peaking phenomenon and noise sensitivity in the application of the High-Gain observer, a parameter tuning method based on the LPV/LMI approach for a 2nd-order cascade observer structure is proposed in this paper. Compared to other high-gain observer methods, this method can significantly reduce the infimum of gain in the observer, thereby reducing the peak phenomenon of state estimation and the influence of measurement output noise. By transforming the observer structure into a Luenberger-like structure, the parameters of the observer can be solved by one linear matrix inequality (LMI) with a high-gain effect or a 2n of LMI sets (LMIs) without a high-gain effect. Then by decomposing the nonlinear part of the system dynamics into high-dimensional and low-dimensional parts, we could solve the adjustable number 2 j s of LMIs can be solved to obtain the result with limited high-gain effect. Stability analysis based on the Lyapunov method proves the convergence of this method, and the effectiveness of this method is verified through applications to one single-link mechanical arm model and a vehicle trajectory estimation application.