scholarly journals Global Exponential Stability of Discrete-Time Neural Networks with Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
S. Udpin ◽  
P. Niamsup
Keyword(s):  
Neural Networks ◽  
Global Stability ◽  
Discrete Time ◽  
Type Inequality ◽  
Discrete Systems ◽  
Nonlinear Difference Equation ◽  
Time Varying ◽  
Stability Criteria ◽  
Nonlinear Discrete Systems ◽  
Theoretical Results

This paper presents some global stability criteria of discrete-time neural networks with time-varying delays. Based on a discrete-type inequality, a new global stability condition for nonlinear difference equation is derived. We consider nonlinear discrete systems with time-varying delays and independence of delay time. Numerical examples are given to illustrate the effectiveness of our theoretical results.

Stability analysis for discrete-time neural networks with time-varying delays and stochastic parameter uncertainties

2015 ◽  
Vol 93 (4) ◽  
pp. 398-408 ◽  
Author(s):  
O.M. Kwon ◽  
M.J. Park ◽  
S.M. Lee ◽  
E.J. Cha
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Parameter Uncertainties ◽  
Stochastic Parameter ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper proposes new delay-dependent stability criteria for discrete-time neural networks with interval time-varying delays and probabilistic occurring parameter uncertainties. It is assumed that parameter uncertainties are changed with the environment, explored using random situations, and its stochastic information is included in the proposed method. By constructing a suitable Lyapunov–Krasovskii functional, new delay-dependent stability criteria for the concerned systems are established in terms of linear matrix inequalities, which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed method.

scholarly journals Novel Delay-Dependent Stability Criteria for Discrete-Time Neural Networks with Time-Varying Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Sreten Stojanovic ◽  
Milan Stojanovic ◽  
Milos Stevanovic
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Convex Combination ◽  
Linear Matrix ◽  
Time Varying ◽  
Stability Criteria ◽  
Time Varying Delay ◽  
Reciprocally Convex Combination ◽  
Delay Dependent ◽  
Delay Dependent Stability

The delay-dependent stability problem is investigated for discrete-time neural networks with time-varying delays. A new augmented Lyapunov-Krasovskii functional (LKF) with single and double summation terms and several augmented vectors is proposed by decomposing the time-delay interval into two nonequidistant subintervals to derive less conservative stability conditions. Then, by using Wirtinger-based inequality, reciprocally, and extended reciprocally convex combination lemmas, tight estimations for sum terms in the forward difference of the LKF are given. Several zero equalities are introduced to further relax the existing results. Less conservative stability criteria are proposed in terms of linear matrix inequalities (LMIs). Finally, numerical examples are proposed to show the effectiveness and less conservativeness of the proposed method.

scholarly journals Global Stability of Integral Manifolds for Reaction–Diffusion Delayed Neural Networks of Cohen–Grossberg-Type under Variable Impulsive Perturbations

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1082
Author(s):  
Gani Stamov ◽  
Ivanka Stamova ◽  
George Venkov ◽  
Trayan Stamov ◽  
Cvetelina Spirova
Keyword(s):  
Neural Networks ◽  
Global Stability ◽  
Lyapunov Functions ◽  
Type Inequality ◽  
Reaction Diffusion ◽  
Stability Criteria ◽  
Delayed Neural Networks ◽  
Integral Manifolds ◽  
Impulsive Perturbations ◽  
Impulsive Jumps

The present paper introduces the concept of integral manifolds for a class of delayed impulsive neural networks of Cohen–Grossberg-type with reaction–diffusion terms. We establish new existence and boundedness results for general types of integral manifolds with respect to the system under consideration. Based on the Lyapunov functions technique and Poincarѐ-type inequality some new global stability criteria are also proposed in our research. In addition, we consider the case when the impulsive jumps are not realized at fixed instants. Instead, we investigate a system under variable impulsive perturbations. Finally, examples are given to demonstrate the efficiency and applicability of the obtained results.

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