Abstract
The neural network time-varying delay was described as the dynamic properties of a neural cell, including neural functional and neural delay differential equations. The differential expression explains the derivative term of current and past state. The objective of this paper obtained the neural network time-varying delay. A delay-dependent condition is provided to ensure the considered discrete-time neural networks with time-varying delays to be finite-time stability, dissipativity, and passivity. This paper using a new Lyapunov-Krasovskii functional as well as the free-weighting matrix approach and a linear matrix inequality analysis (LMI) technique constructing to a novel sufficient criterion on finite-time stability, dissipativity, and passivity of the discrete-time neural networks with time-varying delays for improving. We propose sufficient conditions for discrete-time neural networks with time-varying delays. An effective LMI approach derives by base the appropriate type of Lyapunov functional. Finally, we present the effectiveness of novel criteria of finite-time stability, dissipativity, and passivity condition of discrete-time neural networks with time-varying delays in the form of linear matrix inequality (LMI).
Highlights
Current years we have been attending in researching delay neural networks (NNs), this is mainly to the major feasible applications in many areas, for example, combinatorial optimization, static image processing, pattern recognition, associative memory and signal processing [1]
It is significant to learn the stability of discrete-time neural networks (DNNs) with time-varying delay
Based on the newly established integral inequality, a class of new Lyapunov functional including is proposed, and some less conservative delay range-dependent stability, dissipativity and passivity criteria are derived in terms of linear matrix inequality analysis (LMI)
Summary
Current years we have been attending in researching delay neural networks (NNs), this is mainly to the major feasible applications in many areas, for example, combinatorial optimization, static image processing, pattern recognition, associative memory and signal processing [1]. The dissipative theory being a framework for the design and analysis of control systems using an input-output description based on energy-related consideration is applicable in characterizing important system behaviours, such as passivity, and has close connections with passivity theorem, bounded real lemma, Kalman--Yakubovich lemma, and the circle criterion [20,21]. The problem of robust passivity analysis of uncertain NNs with discrete and distributed time-varying delays has been reported, by constructing an augmented Lyapunov functional and combining a new integral inequality with the reciprocally convex approaches respectively. Based on the newly established integral inequality, a class of new Lyapunov functional including is proposed, and some less conservative delay range-dependent stability, dissipativity and passivity criteria are derived in terms of LMIs. This paper is organized as follows.
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