Passive control of chaotic system with multiple strange attractors

In this paper we present a new simple controller for a chaotic system, that is, theNewton--Leipnik equation with two strange attractors: the upper attractor (UA) andthe lower attractor (LA). The controller design is based on the passive technique.The final structure of this controller for original stabilization has a simplenonlinear feedback form. Using a passive method, we prove the stability of aclosed-loop system. Based on the controller derived from the passive principle, weinvestigate three different kinds of chaotic control of the system, separately: theoriginal control forcing the chaotic motion to settle down to the origin from anarbitrary position of the phase space; the chaotic intra-attractor control forstabilizing the equilibrium points only belonging to the upper chaotic attractor orthe lower chaotic one, and the inter-attractor control for compelling the chaoticoscillation from one basin to another one. Both theoretical analysis and simulationresults verify the validity of the suggested method.