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Stability control of fractional chaotic systems based on a simple Lyapunov function. (English) Zbl 1412.93063

Summary: In this paper the stabilization of fractional-order chaotic systems and a new property of fractional derivatives are studied. Then we propose a new fractional-order extension of Lyapunov direct method and a control method based on a simple Lyapunov candidate function. The proposed control method can be applied to the stabilization of fractional-order chaotic and hyperchaotic systems. This control method is simple, universal, and theoretically rigorous. Numerical simulations are given for three fractional-order chaotic (or hyperchaotic) systems to verify the effectiveness and the universality of the proposed control method.

MSC:

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93D15 Stabilization of systems by feedback

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sysdfod; DFOC
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