Stability criteria of discrete-time analog neural networks

2002 ◽  
Author(s):  
Liang Jin ◽  
M.M. Gupta ◽  
P.N. Nikiforuk
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Stability Criteria ◽  
Analog Neural Networks

Robust Stochastic Stability of Discrete-Time Markovian Jump Neural Networks with Leakage Delay

2014 ◽  
Vol 69 (1-2) ◽  
pp. 70-80 ◽  
Author(s):  
Mathiyalagan Kalidass ◽  
Hongye Su ◽  
Sakthivel Rathinasamy
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Stochastic Stability ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Stability Criteria ◽  
Markovian Jumping ◽  
Weighting Matrix ◽  
The Stability ◽  
Delay Dependent

This paper presents a robust analysis approach to stochastic stability of the uncertain Markovian jumping discrete-time neural networks (MJDNNs) with time delay in the leakage term. By choosing an appropriate Lyapunov functional and using free weighting matrix technique, a set of delay dependent stability criteria are derived. The stability results are delay dependent, which depend on not only the upper bounds of time delays but also their lower bounds. The obtained stability criteria are established in terms of linear matrix inequalities (LMIs) which can be effectively solved by some standard numerical packages. Finally, some illustrative numerical examples with simulation results are provided to demonstrate applicability of the obtained results. It is shown that even if there is no leakage delay, the obtained results are less restrictive than in some recent works.

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.

CONVERGENCE OF DISCRETE-TIME RECURRENT NEURAL NETWORKS WITH VARIABLE DELAY

2005 ◽  
Vol 15 (02) ◽  
pp. 581-595 ◽  
Author(s):  
JINLING LIANG ◽  
JINDE CAO ◽  
JAMES LAM
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Discrete Time ◽  
Recurrent Neural Networks ◽  
Matrix Decomposition ◽  
Linear Matrix ◽  
Variable Delay ◽  
Stability Criteria ◽  
Lmi Approach ◽  
The Neural Networks

In this paper, some global exponential stability criteria for the equilibrium point of discrete-time recurrent neural networks with variable delay are presented by using the linear matrix inequality (LMI) approach. The neural networks considered are assumed to have asymmetric weighting matrices throughout this paper. On the other hand, by applying matrix decomposition, the model is embedded into a cooperative one, the latter possesses important order-preserving properties which are basic to our analysis. A sufficient condition is obtained ensuring the componentwise exponential stability of the system with specific performances such as decay rate and trajectory bounds.

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.

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