Abstract
A novel approach is presented to realize the optimal exponential synchronization of nonidentical multiple time-delay chaotic (MTDC) systems via fuzzy control scheme. A neural-network (NN) model is first constructed for 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, a delay-dependent exponential stability criterion of the error system derived in terms of Lyapunov's direct method is proposed to guarantee 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). According to the LMI, a fuzzy controller is synthesized not only to realize the exponential synchronization but also to achieve the optimal performance by minimizing the disturbance attenuation level at the same time. Finally, a numerical example with simulations is given to demonstrate the effectiveness of our approach.
Highlights
The stability analysis and stabilization of time-delay systems are problems of considerable theoretical and practical significance and have attracted the interest of many investigators for several years
With a view to the abovementioned, a novel approach is proposed via the neural-network-(NN-) based technique to realize the optimal H∞ exponential synchronization of nonidentical multiple time-delay chaotic (MTDC) systems such that the trajectories of the slave systems can approach those of the master systems and the effect of external disturbances on the control performance can be attenuated to a minimum level
A linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model
Summary
The stability analysis and stabilization of time-delay systems are problems of considerable theoretical and practical significance and have attracted the interest of many investigators for several years. The problem of chaos synchronization between two different uncertain chaotic systems is an important research issue [12] He et al [13] investigate synchronization of two nonidentical chaotic systems with time-varying delay and parameter mismatches via impulsive control. With a view to the abovementioned, a novel approach is proposed via the neural-network-(NN-) based technique to realize the optimal H∞ exponential synchronization of nonidentical multiple time-delay chaotic (MTDC) systems such that the trajectories of the slave systems can approach those of the master systems and the effect of external disturbances on the control performance can be attenuated to a minimum level.
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