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On stabilizing \(n\)-dimensional chaotic systems. (English) Zbl 1129.93507

Summary: This paper deals with the control of a class of \(n\)-dimensional chaotic systems. The proposed method consists in a Variable Structure Control approach based on system energy consideration for both controller design and system stabilization. First, we present some theoretical results related to the stabilization of global invariant sets included in a selected two-dimensional subspace of the state space. Then, we define some conditions, involving both system definition and control law design, under which the stabilized orbits can be maintained in a neighborhood of an invariant, nondegenerate, closed conic section (i.e. an ellipse or a circle). Finally, an example related to the chaotic circuit of Chua is given.

MSC:

93D15 Stabilization of systems by feedback
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N35 Dynamical systems in control
93C10 Nonlinear systems in control theory
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