An extension to chaos control via Lie derivatives: Fully linearizable systems

The technique of using Lie derivatives to control chaos introduced by Kocarev et al. [Chaos, Solitons Fractals 9, 1359-1366 (1998)] is extended in this contribution. Here, by using Lie derivatives in an extended space state, it is proved that chaos can be practically suppressed via feedback in spite of the Lie derivative being ill-posed at the reference. The main idea is to construct a dynamically equivalent system. In this way, the chaotic system can be practically stabilized around any point of singularity x(0). The Lorenz equation is used as an illustrative example to show the application in the chaos control context. (c) 2002 American Institute of Physics.