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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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\textit{H. Wang} et al., Commun. Nonlinear Sci. Numer. Simul. 14, No. 4, 1410--1417 (2009; Zbl 1221.93049)

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