In this paper, the authors focus on the application of linear matrix inequality (LMI) in the stabilization of fractional-order chaotic systems and the strict mathematical description and proof of LMI. Based on the theory of the fractional-order interval system, the generalized Takagi-Sugeno fuzzy model is applied to a wide class of fractional-order chaotic systems with uncertain parameters. The sufficient stability condition for the fractional-order systems is presented as a set of LMI for the first time and the strict mathematical norms of LMI are given. Furthermore, a controller is developed to stabilize fractional-order chaotic systems, and may be applied to fractional-order systems with uncertainty. Finally, two representative examples of the three-dimensional fractional-order permanent magnet synchronous motor system and the four-dimensional fractional-order hyperchaotic system based on Chen’s system are provided to demonstrate the effectiveness of theoretical analysis.
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