Optimal Exponential Synchronization of Chaotic Systems with Multiple Time Delays via Fuzzy Control

Feng-Hsiag Hsiao
2013 Abstract and Applied Analysis  
This study presents an effective approach to realize the optimal H ∞ exponential synchronization of multiple time-delay chaotic (MTDC) systems. First, a neural network (NN) model is employed to approximate the MTDC system. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. Based on this LDI state-space representation, this study proposes a delay-dependent exponential stability criterion of the error system derived in terms of
more » ... yapunov's direct method to ensure that the trajectories of the slave system can approach those of the master system. Subsequently, the stability condition of this criterion is reformulated into a linear matrix inequality (LMI). Based on the LMI, a fuzzy controller is synthesized not only to realize the exponential synchronization but also to achieve the optimal H ∞ performance by minimizing the disturbance attenuation level. Finally, a numerical example with simulations is provided to illustrate the concepts discussed throughout this work.
doi:10.1155/2013/742821 fatcat:xpamdl4sfjbobmgaispzm52eiu