Stability in cellular neural networks with a piecewise constant argument

Abstract

Differential equations with a piecewise constant argument of generalized type Lyapunov-Razumikhin technique Method of Lyapunov functions Linear matrix inequality a b s t r a c tIn this paper, by using the concept of differential equations with piecewise constant arguments of generalized type [1-4], a model of cellular neural networks (CNNs) [5,6] is developed. The Lyapunov-Razumikhin technique is applied to find sufficient conditions for the uniform asymptotic stability of equilibria. Global exponential stability is investigated by means of Lyapunov functions. An example with numerical simulations is worked out to illustrate the results.

Analysis and Design of Associative Memories for Memristive Neural Networks with Deviating Argument

“…For neural network model (1), the conventional definition of solution for differential equations cannot apply here. To tackle this problem, the solution concept for differential equations with deviating argument is introduced [24][25][26][27][28][29][30]. According to this theory, a solution ( ) = ( 1 ( ), 2 ( ), .…”

“…For the past few years, hybrid dynamic systems have remained one of the most active fields of research in the control community [22][23][24][25][26][27][28][29][30]. For instance, to describe the stationary distribution of temperature along the length of a wire that is bended, the nonlinear dynamic model with deviating argument is often used.…”

Stabilization control of generalized type neural networks with piecewise constant argument

“…Due to its potential applications in various fields, generalized type system with piecewise constant argument has been widely investigated in recent years ( [1][2][3][4][5][6][7]). Different from that the traditional system can only be delayed or advanced, generalized type system can change its type of deviation of the parameters during the motion, and hence can be both delayed and advanced.…”

“…As a special case of the generalized type system, more research has been carried out on the generalized type neural network with piecewise constant argument. Several interesting results on stability analysis of this type of neural networks are presented ( [5][6][7]9]). In [5], the stability of generalized type recurrent neural networks with piecewise constant argument was considered.…”

“…In [5], the stability of generalized type recurrent neural networks with piecewise constant argument was considered. In [6], sufficient conditions on uniform asymptotic stability and global exponential stability of the cellular neural networks with piecewise constant argument were obtained. It was addressed the stability of the impulsive Hopfieldtype neural networks with piecewise constant argument in [7].…”