Stabilization control of generalized type neural networks with piecewise constant argument

Abstract

The generalized type neural networks have always been a hotspot of research in recent years. This paper concerns the stabilization control of generalized type neural networks with piecewise constant argument. Through three types of stabilization control rules (single state stabilization control rule, multiple state stabilization control rule and output stabilization control rule), together with the estimate of the state vector with piecewise constant argument, several succinct criteria of stabilization are derived. The obtained results improve and extend some existing results. Two numerical examples are proposed to substantiate the effectiveness of the theoretical 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.…”

“…Because of this property, related works on the control strategies for nonlinear systems with deviating argument are relatively rare. Viewed from systems involving the interplay, differential equations and difference equations are included in the nonlinear systems with deviating argument [28][29][30]. However, it is still obvious that many basic issues on nonlinear systems with deviating argument remain to be addressed, such as nonlinear dynamics, systems design, and analysis.…”

Razumikhin-type theorems for impulsive differential equations with piecewise constant argument of generalized type

“…Akhmet [18][19][20] generalized the concept of DEPCA by considering arbitrary piecewise constant functions as arguments; the proposed approach overcomes the limitations in the previously used method of study, namely reduction to discrete equations. Afterward, the results of the theory have been further developed [21,22] and applied for qualitative anal-ysis and control problem of real models, for example, in neural network models with or without impulsive perturbations [23][24][25][26][27][28][29][30][31][32][33], which have great significance in solving engineering and electronic problems.…”

Advances in Modelling, Analysis, and Design of Delayed Systems

“…J.-E. Zhang in his paper "Analysis and Design of Associative Memories for Memristive Neural Networks with Deviating Argument" investigates associative memories for memristive neural networks with deviating argument [23]. Firstly, the existence and uniqueness of solution for memristive neural networks with deviating argument are discussed.…”