Active-Passive Decomposition with Application to Arrays of Chaotic Systems

In this paper an alternate method of Active–Passive Decomposition of chaotic systems based on the notion of passivity is presented. The concepts of model following in control theory are applied to show how such a decomposition is useful in achieving synchronization. Besides the fact that model following control may be implemented in a whole class of systems, it is also the basis for designing adaptive systems where the convergence of the scheme is often proved by the use of passivity concepts. The method is shown to be extremely useful in synchronizing passively coupled chaotic systems in general and arrays of coupled but identical controlled chaotic systems in particular.