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To overcome the difficulties in the stability analysis and stabilization for nonlinear fractional systems, the comparison principle for fractional-order systems with Caputo fractional derivatives is constructed, which can simplify the processes of stability analysis and stabilization controller design in a great degree. To verify the feasibility of the proposed method, the problem of stabilizing the...
A generalized Caputo fractional derivative definition is first proposed. Based on that, two comparison inequalities for scalar and vector nonlinear fractional-order systems are constructed, respectively. An example is provided to show how the tools be used to analyze the stability of nonlinear fractional-order systems.
Chaotic synchronization is the key technique in secure communication systems. This paper proposes a novel control method to synchronize two nonidentical discrete-time hyperchaotic maps based on T-S fuzzy models. Firstly, a universal fuzzy modeling process is presented for most discrete-time hyperchaotic maps. Then, a simple fuzzy controller is designed based on the PDC technique. The asymptotic stability...
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