${\rm H}_{\infty }$ State Estimation for Discrete-Time Chaotic Systems Based on a Unified Model

This paper is concerned with the problem of state estimation for a class of discrete-time chaotic systems with or without time delays. A unified model consisting of a linear dynamic system and a bounded static nonlinear operator is employed to describe these systems, such as chaotic neural networks, Chua´s circuits, Hénon map, etc. Based on the H_∞ performance analysis of this unified model using the linear matrix inequality approach, H_∞ state estimator are designed for this model with sensors to guarantee the asymptotic stability of the estimation error dynamic systems and to reduce the influence of noise on the estimation error. The parameters of these filters are obtained by solving the eigenvalue problem. As most discrete-time chaotic systems with or without time delays can be described with this unified model, H_∞ state estimator design for these systems can be done in a unified way. Three numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes.