Abstract
Chaos in Shimizu–Morioka system is controlled by applying a Lie algebraic exact linearization technique. In this state space exact linearization method, a non-linear feedback control law is designed which induces a coordinate transformation thereby changing the original non-linear chaotic system into a linear controllable one. The controller is designed for an arbitrary output and the paper discusses the case of both linear and non-linear outputs. Necessary and sufficient conditions are derived for stabilization of the system to a point and onto a limit cycle. Numerical simulation has been conducted for all these aspects of the problem that conclusively establishes our analytical findings.
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