Exponential H∞ synchronization and state estimation for chaotic systems via a unified model

In this paper, H∞ synchronization and state estimation problems are considered for different types of chaotic systems. A unified model consisting of a linear dynamic system and a bounded static nonlinear operator is employed to describe these chaotic systems, such as Hopfield neural networks, cellular neural networks, Chua's circuits, unified chaotic systems, Qi systems, chaotic recurrent multilayer perceptrons, etc. Based on the H∞ performance analysis of this unified model using the linear matrix inequality approach, novel state feedback controllers are established not only to guarantee exponentially stable synchronization between two unified models with different initial conditions but also to reduce the effect of external disturbance on the synchronization error to a minimal H∞ norm constraint. The state estimation problem is then studied for the same unified model, where the purpose is to design a state estimator to estimate its states through available output measurements so that the exponential stability of the estimation error dynamic systems is guaranteed and the influence of noise on the estimation error is limited to the lowest level. The parameters of these controllers and filters are obtained by solving the eigenvalue problem. Most chaotic systems can be transformed into this unified model, and H∞ synchronization controllers and state estimators for these systems are designed in a unified way. Three numerical examples are provided to show the usefulness of the proposed H∞ synchronization and state estimation conditions.