Optimal H _∞ filtering for discrete-time-delayed chaotic systems via a unified model

This paper presents a unified model, consisting of a linear dynamic system and a bounded static nonlinear operator. Most discrete-time chaotic systems, such as chaotic neural networks, Chua's circuits, and Hénon map etc, can be transformed into this unified model. Based on the H _∞ performance analysis of the estimation error system between the unified model and its improved Luenberger-like filter using the linear matrix inequality (LMI) approach, the optimal H _∞ filter are designed to estimate the states of discrete-time chaotic systems with external disturbance. The H _∞ filter not only guarantees the asymptotic stability of the estimation error system, but also reduces the influence of noise on the estimation error. Two numerical examples are exploited to illustrate the effectiveness of the proposed filter design schemes.