Global Lagrange stability for neutral type neural networks with mixed time-varying delays
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ORIGINAL ARTICLE
Global Lagrange stability for neutral type neural networks with mixed time-varying delays Zhengwen Tu1 • Liangwei Wang1
Received: 30 November 2015 / Accepted: 7 May 2016 Ó Springer-Verlag Berlin Heidelberg 2016
Abstract In this paper, the global exponential stability in Lagrange sense for neutral type neural networks with mixed time-varying delays is studied. By constructing proper Lyapunov functions and using inequality techniques, new delay-dependent succinct criteria are derived to ensure the global exponential Lagrange stability for the aforementioned neural networks. Meanwhile, globally exponentially attractive sets are given out. The results obtained here are more general than some of existing results. Finally, two examples are presented and analyzed to validate our results. Keywords Neural networks Lagrange exponential stability Neutral Time delay
1 Introduction Neural networks have been applied successfully in various areas, such as information processing, automatic control engineering, economics, etc. As is well known, time delays inevitably exist both in artificial and biological neural systems on account of integration and communication delays. Delays are often the sources of poor performances such as instability, chaos, oscillations, etc. Whereas when considering the synchronization problem for complex network, the synchronous ability can be enhanced by introducing proper
& Liangwei Wang [email protected] Zhengwen Tu [email protected] 1
Key Laboratory for Nonlinear Science and System Structure, and School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404100, China
delays [1]. Consequently, we should investigate characteristics of delays to solve corresponding problems more reasonably [1–10]. The stability of neural networks with time delays have been investigated in [3–6]. The global stability of complex neural networks was also considered in [7, 8]. Song and Zhao have discussed the global exponential stability for complex-valued neural networks on time scales [8]. Lu and Chen have investigated the synchronization problem of neural networks with delays [9]. In practical applications, there likely exist distribution of conduction velocities along pathways and distribution of propagation delays due to the existence of multitudinous parallel pathways with multifarious axon sizes and lengths in neural networks. On this occasion, the signal transmission is not instantaneous and discrete delays can not simulate them properly. A more appropriate way is to merge continuously distributed delays into neural networks models [11]. Therefore, dynamical properties of neural networks with discrete and distributed delays have been studied extensively by scientific and technical workers [11–15]. Actually, dynamics behaviors of certain practical systems depend on delays of state as well as delays of state derivative, and such systems are known as neutral systems. They are often appeared in various fields such as automatic control, population ecology, and heat exch
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