Producing Stable Periodic Solutions of Switched Impulsive Delayed Neural Networks Using a Matrix-Based Cubic Convex Combination Approach

2020 ◽  
pp. 1-15
Author(s):  
Peng Wan ◽  
Dihua Sun ◽  
Min Zhao
Keyword(s):  
Neural Networks ◽  
Periodic Solutions ◽  
Convex Combination ◽  
Delayed Neural Networks ◽  
Stable Periodic ◽  
Combination Approach

scholarly journals Stability Analysis for Delayed Neural Networks: Reciprocally Convex Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Hongjun Yu ◽  
Xiaozhan Yang ◽  
Chunfeng Wu ◽  
Qingshuang Zeng
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Convex Combination ◽  
Linear Matrix ◽  
Delayed Neural Networks ◽  
Time Varying Delay ◽  
Reciprocally Convex Combination ◽  
Combination Approach ◽  
Continuous Neural Networks ◽  
Delay Dependent

This paper is concerned with global stability analysis for a class of continuous neural networks with time-varying delay. The lower and upper bounds of the delay and the upper bound of its first derivative are assumed to be known. By introducing a novel Lyapunov-Krasovskii functional, some delay-dependent stability criteria are derived in terms of linear matrix inequality, which guarantee the considered neural networks to be globally stable. When estimating the derivative of the LKF, instead of applying Jensen’s inequality directly, a substep is taken, and a slack variable is introduced by reciprocally convex combination approach, and as a result, conservatism reduction is proved to be more obvious than the available literature. Numerical examples are given to demonstrate the effectiveness and merits of the proposed method.

Multiple Almost Periodic Solutions in Nonautonomous Delayed Neural Networks

2007 ◽  
Vol 19 (12) ◽  
pp. 3392-3420 ◽  
Author(s):  
Kuang-Hui Lin ◽  
Chih-Wen Shih
Keyword(s):  
Neural Networks ◽  
Periodic Solutions ◽  
Contraction Mapping Principle ◽  
Time Lags ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Neuron Network ◽  
Delayed Neural Networks ◽  
External Bias ◽  
Exponentially Stable

A general methodology that involves geometric configuration of the network structure for studying multistability and multiperiodicity is developed. We consider a general class of nonautonomous neural networks with delays and various activation functions. A geometrical formulation that leads to a decomposition of the phase space into invariant regions is employed. We further derive criteria under which the n-neuron network admits 2n exponentially stable sets. In addition, we establish the existence of 2n exponentially stable almost periodic solutions for the system, when the connection strengths, time lags, and external bias are almost periodic functions of time, through applying the contraction mapping principle. Finally, three numerical simulations are presented to illustrate our theory.

Improved Results on Finite-Time Stability Analysis of Neural Networks With Time-Varying Delays

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
S. Saravanan ◽  
M. Syed Ali
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Finite Time ◽  
Lyapunov Functional ◽  
Convex Combination ◽  
Linear Matrix ◽  
Time Stability ◽  
Delayed Neural Networks ◽  
Finite Time Stability ◽  
Combination Methods

This paper investigates the issue of finite time stability analysis of time-delayed neural networks by introducing a new Lyapunov functional which uses the information on the delay sufficiently and an augmented Lyapunov functional which contains some triple integral terms. Some improved delay-dependent stability criteria are derived using Jensen's inequality, reciprocally convex combination methods. Then, the finite-time stability conditions are solved by the linear matrix inequalities (LMIs). Numerical examples are finally presented to verify the effectiveness of the obtained results.

scholarly journals Stability Analysis of Quaternion-Valued Neutral-Type Neural Networks with Time-Varying Delay

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 101 ◽  
Author(s):  
Jinlong Shu ◽  
Lianglin Xiong ◽  
Tao Wu ◽  
Zixin Liu
Keyword(s):  
Neural Networks ◽  
Convex Combination ◽  
Neutral Type ◽  
Stability Conditions ◽  
Time Varying ◽  
Time Varying Delay ◽  
Convex Inequality ◽  
Inequality Technique ◽  
Combination Approach ◽  
Complex Valued

This paper addresses the problem of global μ -stability for quaternion-valued neutral-type neural networks (QVNTNNs) with time-varying delays. First, QVNTNNs are transformed into two complex-valued systems by using a transformation to reduce the complexity of the computation generated by the non-commutativity of quaternion multiplication. A new convex inequality in a complex field is introduced. In what follows, the condition for the existence and uniqueness of the equilibrium point is primarily obtained by the homeomorphism theory. Next, the global stability conditions of the complex-valued systems are provided by constructing a novel Lyapunov–Krasovskii functional, using an integral inequality technique, and reciprocal convex combination approach. The gained global μ -stability conditions can be divided into three different kinds of stability forms by varying the positive continuous function μ ( t ) . Finally, three reliable examples and a simulation are given to display the effectiveness of the proposed methods.

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