Abstract
In this paper, an integral sliding mode control approach is presented to investigate synchronization of nonidentical chaotic neural networks with discrete and distributed time-varying delays as well as leakage delay. By considering a proper sliding surface and constructing Lyapunov-Krasovskii functional, as well as employing a combination of the free-weighting matrix method, Newton-Leibniz formulation and inequality technique, a sliding mode controller is designed to achieve the asymptotical synchronization of the addressed nonidentical neural networks. Moreover, a sliding mode control law is also synthesized to guarantee the reachability of the specified sliding surface. The provided conditions are expressed in terms of linear matrix inequalities, and are dependent on the discrete and distributed time delays as well as leakage delay. A simulation example is given to verify the theoretical results.
Highlights
In the past few years, neural networks have attracted much attention due to the background of a wide range applications such as associative memory, pattern recognition, image processing and model identification [1]
In [35], the projective synchronization for two nonidentical chaotic neural networks with constant delay was investigated, a delay-dependent sufficient condition was derived by sliding mode control approach, linear matrix inequality (LMI) technique and Lyapunov stability theory
The provided conditions are expressed in terms of LMI, and are dependent on the discrete and distributed time delays as well as leakage delay
Summary
In the past few years, neural networks have attracted much attention due to the background of a wide range applications such as associative memory, pattern recognition, image processing and model identification [1]. In [33], an integral sliding mode control approach is proposed to address synchronization for two nonidentical chaotic neural networks with constant delay. In [35], the projective synchronization for two nonidentical chaotic neural networks with constant delay was investigated, a delay-dependent sufficient condition was derived by sliding mode control approach, LMI technique and Lyapunov stability theory. Differing from the results in [33,34,35], the main contributions of this study are to investigate the effect of the leakage delay on the synchronization of two nonidentical chaotic neural networks with discrete and distributed time-varying delays as well as leakage delay and to propose an integral sliding mode control approach to solving it. + B1h(x(t − τ (t))) + C1 h(x(s))ds
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