Exponential Stabilization of Neural Networks With Various Activation Functions and Mixed Time-Varying Delays

Abstract

This paper presents some results on the global exponential stabilization for neural networks with various activation functions and time-varying continuously distributed delays. Based on augmented time-varying Lyapunov-Krasovskii functionals, new delay-dependent conditions for the global exponential stabilization are obtained in terms of linear matrix inequalities. A numerical example is given to illustrate the feasibility of our results.

Finite time stabilization of delayed neural networks

“…On one hand, our results complement and extend the previous results in Liu et al (2013Liu et al ( , 2014a where delays are not taken into consideration in studying finite time stability problem. On the other hand, the new proposed results here achieve a valuable improvement compared with the present works (Chen et al, 2014;Guo & Wang, 2013;Huang et al, 2013;Huang & Li, 2009;Hu et al, 2010;Phat & Trinh, 2010;Wen et al, 2015;Wu & Zeng, 2012; where only exponential or asymptotic stabilization of DNNs is obtained in these papers.…”

“…Although stabilization of DNNs has been investigated in the past few years (Chen et al, 2014;Guo & Wang, 2013;Huang et al, 2013;Huang & Li, 2009;Hu et al, 2010;Phat & Trinh, 2010;Wen et al, 2015;Wu & Zeng, 2012;, so far, there is little work concerning the finite time stabilization of DNNs. In this paper, two different kinds of feedback control law are designed and some sufficient conditions in Theorem 2 and 3 are given to ensure the finite time stabilization of DNNs.…”

“…During the past decades, stability analysis of delayed neural networks (DNNs) has been extensively investigated and many useful stability criteria have been established (Cao & Wang, 2005;Faydasicok & Arik, 2012;Forti et al, 2005;He & Wu, 2006;Huang et al, 2012;Shen & Wang, 2009Wang & Liu, 2005;Wang et al, 2006;Lu, 2002;Zeng & Zheng, 2012). On the other hand, the stabilization of DNNs has been attracting considerable attention and several feedback stabilizing control methods have been proposed, such as linear control (Guo & Wang, 2013;Huang et al, 2013;Phat & Trinh, 2010;Wen et al, 2015;Wu & Zeng, 2012), impulsive control (Guan & Zhang, 2008), and intermittent control (Chen et al, 2014;Huang & Li, 2009;Hu et al, 2010;.…”

Stabilization control of generalized type neural networks with piecewise constant argument

“…In [15], the output feedback stabilization was explored on the type of delayed nonlinear interconnected systems. In [25,29], the state vector was chosen as the component of the controller to stabilize the neural network. Whereas, the models of the neural networks concerned above are either about constant delays, or about time-varying delays, or about distributed delays.…”

Exponential Synchronization of Master-Slave Neural Networks With Mixed Time-Varying Delays via Hybrid Intermittent Feedback Control

“…When neural networks are created for problem solving, it is desirable for their activation functions are not too restrictive. As a result, there has been considerable research work on the stability of neural networks with various activation functions and more general conditions [5,6]. The first concept of chaos synchronization is making two chaotic systems oscillate in a synchronized manner was introduced by [2] and many different methods have been applied theoretically and experimentally to synchronize chaotic systems, for example active control [7], adaptive control [7], time-delay feedback control [?, 8] and intermittent control [9], etc.…”