H∞ state estimation for a unified chaotic system with uncertainty

The unified chaotic system incorporates the behaviors of the Lorenz, the Chen and the Lü chaotic systems. In this paper, the H∞ state estimation problem is investigated for a unified chaotic system with uncertainty (noise perturbation). The unified chaotic system is first transformed into a Lur´e system. Based on the H∞ performance analysis for the Lur´e system, an improved Luenberger-like estimator (or filter) is designed to estimate its states through available output measurements such that the exponential stability of the estimation error dynamic systems is guarantee and the influence of noise on the estimation error is limited within a lowest level. The parameters of the estimator (or filter) are obtained by solving the eigenvalue problem (EVP). A numerical example is provided to show the usefulness of the proposed estimation method.