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Sliding mode control for chaotic systems based on LMI. (English) Zbl 1221.93049

Summary: We investigate the chaos control problem for a general class of chaotic systems. A feedback controller is established to guarantee asymptotical stability of the chaotic systems based on the sliding mode control theory. A new reaching law is introduced to solve the chattering problem that is produced by traditional sliding mode control. A dynamic compensator is designed to improve the performance of the closed-loop system in sliding mode, and its parameter is obtained from a linear matrix inequality (LMI). Simulation results for the well known Chua’s circuit and Lorenz chaotic system are provided to illustrate the effectiveness of the proposed scheme.

MSC:

93B12 Variable structure systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34H10 Chaos control for problems involving ordinary differential equations
93B52 Feedback control
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