Linear matrix inequality criteria for robust synchronization of uncertain fractional-order chaotic systems

This paper is devoted to synchronization of uncertain fractional-order chaotic systems with fractional-order alpha: 0 < alpha < 1 and 1 <= alpha < 2, respectively. On the basis of the stability theory of fractional-order differential system and the observer-based robust control, two sufficient and necessary conditions for synchronizing uncertain fractional-order chaotic systems with parameter perturbations are presented in terms of linear matrix inequality, which is an efficient method and could be easily solved by the toolbox of MATLAB. Finally, fractional-order uncertain chaotic Lu system with fractional-order alpha = 0.95 and fractional-order uncertain chaotic Lorenz system with fractional-order alpha = 1.05 are taken as numerical examples to show the validity and feasibility of the proposed method. (C) 2011 American Institute of Physics. [doi:10.1063/1.3650237]