Stability of Neural Networks With Random Impulses

Abstract

One of the main properties of solutions of neural networks is stability and often the direct Lyapunov method is used to study stability properties. We consider the Hopfield's graded response neural network in the case when the neurons are subject to a certain impulsive state displacement at random exponentially distributed moments. It changes significantly the behavior of the solutions because they are not deterministic ones but they are stochastic processes. We examine the stability of the equilibrium of the model. Some sufficient conditions for p-moment stability of equilibrium of neural networks with time varying self-regulating parameters of all units and time varying functions of the connection between two neurons in the network are obtained. These sufficient conditions are explicitly expressed in terms of the parameters of the system and hence they are easily verifiable. We illustrate our theory on a particular nonlinear neural network.

Stability and guaranteed cost control for linear impulsive systems with random impulses: Application to stochastic event‐triggered control

“…where Ah , and Q = ∫ h 0 e A T s Qe As ds, then system (1) can be stabilized by (12) with K = KX −1 . Meanwhile, the guaranteed cost function satisfies  ≤ x T 0 X −1 x 0 .…”

Stability analysis based on a control adjuster for switched neural networks by trajectory similarity

“…In particular, the neural networks, whose system stability results possess relative conservatism, have some limitations in application, mainly in that it is not easy to control the state output of the neural networks. A great deal of valuable theoretical results (see earlier research [20–26]) have been achieved for this kind of neural networks. The other type is the system stabilization research of neural networks with controller, in which the controller is generally designed associating with the system state, that is, $$$ K\left(t,x(t)\right) $$$.…”

“…However, Lyapunov conducted stability analysis from the perspective of energy; that is to say, the stability of the system is determined based on the derivative value of the positive definite function. Up to now, a large number of theoretical study results have been achieved based on Lyapunov-Krasovskii functional for many kinds of neural networks, such as earlier studies [10,12,22] and previous research [33][34][35]. It should be pointed out that in the general stability simulation of the neural networks, the system trajectory always evolve from the initial value to the final result to be a black box.…”

Exponential Stability Analysis and Application of Parameters Switched Neural Networks Via Intermittent Observation and Feedback Control

“…It should be pointed out that artificial neural networks can exhibit some complicated dynamics and even chaotic behaviors, the stability of stochastic neural networks has also become an important area of study. The theoretical research of stochastic neural networks mainly includes stability analysis (see [8][9][10][11][12]) and synchronous control (see [13][14][15]). Among them, the stability analysis of neural networks, such as asymptotical stability [16,17], mean square stability [18,19] and X.-H. Zhou is with the School of Mathematics and Statistics, Anhui Normal University, Wuhu 241000, Anhui, China (e-mail: zhouxh8762@163.com).…”

“…The stability research of stochastic system by the method of Lyapunov-Krasovskii functional, which has attracted a large number of scholars to study the stability problem of neural networks, (see [12,16,19,20] and [22][23][24][25][26]). For example, in [12], some sufficient conditions for p-moment stability of equilibrium of neural networks with time varying self-regulating parameters are obtained, and the main stability results based on the properties of solutions of neural networks are acquired by using Lyapunov method. The mean square exponential inputto-state stability in [20] for stochastic delay reaction-diffusion neural networks are investigated via the help of Lyapunov-Krasovskii functional method and Wirtinger-type inequality.…”