Abstract
In this paper, the stability problem is studied for inertial neural network with time-varying delays. The sampled-data control method is employed for the system design. First, by choosing a proper variable substitution, the original system is transformed into first-order differential equations. Then, an input delay approach is applied to deal with the stability of sampling system. Based on the Lyapunov function method, several sufficient conditions are derived to guarantee the global stability of the equilibrium. Furthermore, when employing an error-feedback control term to the slave neural network, parallel criteria regarding to the synchronization of the master neural network are also generated. Finally, some examples are given to illustrate the theoretical results.
Highlights
Recurrent neural networks (RNNS), especially Hopfield neural networks, cellular neural networks (CNNs), Cohen–Grossberg neural networks (CGNNs), bidirectional associative memory (BAM) neural networks have been extensively investigated during the past years, since their potential application in the fields of pattern recognition, associative memories, signal processing, fixed-point computations, and so on
It has been confirmed that the time delay, which is an inherent feature of signal transmission between neurons, is one of the main sources for causing oscillation, divergence or instability of neural networks
We shall establish some sufficient conditions to ensure the stability of network (2.9)
Summary
Recurrent neural networks (RNNS), especially Hopfield neural networks, cellular neural networks (CNNs), Cohen–Grossberg neural networks (CGNNs), bidirectional associative memory (BAM) neural networks have been extensively investigated during the past years, since their potential application in the fields of pattern recognition, associative memories, signal processing, fixed-point computations, and so on. In [18], the matrix measure strategies were used to analyze the stability and synchronization of inertial BAM neural network with time delays. Stability of inertial BAM neural network with time-varying delay was studied via impulsive control [19]. The stabilization of BAM neural networks with time-varying delay in the leakage terms was studied via sampled-data control [14]. Using sampled-data control, the asymptotical synchronization problem of Chaotic Lur’e systems with time delays was investigated in [31]. Motivated by the above discussions, this paper mainly focuses on the fundamental problem of stability discussion of a class of time-varying delayed inertial neuron network via sampleddata control. (1) We make the first attempt to address the sampled-data stability control problem for inertial neuron networks with time-varying delays.
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