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Projective synchronization of different chaotic time-delayed neural networks based on integral sliding mode controller. (English) Zbl 1200.65103

Summary: An integral sliding mode control approach is presented to study the projective synchronization for different chaotic time-delayed neural networks. A sliding mode surface is appropriately constructed and a sliding mode controller is synthesized to guarantee the reachability of the specified sliding surface. The global asymptotic stability of the error dynamical system in the specified switching surface is investigated with the Lyapunov-Krasovskii (L-K) functional method. A delay-dependent sufficient condition is derived and the maximum time-delay value is obtained by means of the linear matrix inequality (LMI) technique. A simulation example is finally exploited to illustrate the feasibility and effectiveness of the proposed approach, verify the conservativeness of L-K method and LMI technique, and exhibit the relationship between the convergence velocity of error system and the gain matrix.

MSC:

65P20 Numerical chaos
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
65L03 Numerical methods for functional-differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
37M05 Simulation of dynamical systems
65L20 Stability and convergence of numerical methods for ordinary differential equations
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