Further analysis of global robust stability of neural networks with multiple time delays
Section snippets
System description and preliminaries
In recent years, neural networks have been widely used in solving various classes of engineering problems such as signal processing, optimization, image processing, associative memory design and control systems. In such applications, it is important to know the global stability properties of the designed neural network, which makes the analysis of dynamical behavior of neural networks one of the key factors in the design and applications of neural networks. Therefore, there has been a great
Global robust stability analysis
In this section, we present a theorem which states the conditions that guarantee the existence, uniqueness and global asymptotic stability of the equilibrium point of system (1) under the parameter uncertainties given by Eq. (2). Before we proceed any further, in order to simplify the proofs of the stability part of the theorem, we will shift the equilibrium point of system (1) to the origin by using the transformation , . This transformation puts the system (1) in
Comparison and examples
In this section, by giving some constructive numerical examples, we will compare our results with the previous robust stability result derived in the literature. In order to make a precise comparison, we first restate the previous literature results obtained for the robust stability of neural network model (1): Theorem 2 Let . Then, the neural network model (1) is globally asymptotically robust stable, if the following condition holds: where and Ozcan and Arik [2]
Conclusions
The main contribution of this paper is the result that ensures the existence, uniqueness and global robust stability of equilibrium point for neural networks with multiple time delays with respect to the Lipschitz activation functions. The obtained condition has established a relationship between the network parameters of neural system and is independently of the delay parameters. A comparison between the result of this paper and the corresponding robust stability results derived in the
References (47)
- et al.
New results for robust stability of dynamical neural networks with discrete time delays
Expert Systems with Applications
(2010) - et al.
An analysis of global robust stability of neural networks with discrete time delays
Physics Letters A
(2006) - et al.
Global robust stability of interval cellular neural networks with time-varying delays
Chaos, Solitons and Fractals
(2005) - et al.
Improved global robust exponential stability criteria for interval neural networks with time-varying delays
Expert Systems with Applications
(2011) - et al.
Global exponential robust stability of static interval neural networks with S-type distributed delays
Journal of the Franklin Institute
(2011) - et al.
Robust delay-dependent exponential stability for uncertain stochastic neural networks with mixed delays
Neurocomputing
(2011) Robust stability of delayed fuzzy Cohen–Grossberg neural networks
Computers and Mathematics with Applications
(2011)- et al.
Improved results on robust exponential stability criteria for neutral-type delayed neural networks
Applied Mathematics and Computation
(2010) - et al.
Robust state estimation for discrete-time stochastic neural networks with probabilistic measurement delays
Neurocomputing
(2010) - et al.
Robust stability of uncertain fuzzy cellular neural networks with time-varying delays and reaction diffusion terms
Neurocomputing
(2010)
New LMI-based criteria for global robust stability of delayed neural networks
Applied Mathematical Modelling
Global robust stability for stochastic interval neural networks with continuously distributed delays of neutral type
Applied Mathematics and Computation
Modified criteria for global robust stability of interval delayed neural networks
Applied Mathematics and Computation
LMI conditions for global robust stability of delayed neural networks with discontinuous neuron activations
Applied Mathematics and Computation
Global stability analysis of interval neural networks with discrete and distributed delays of neutral type
Expert Systems with Applications
Robust stability analysis for discrete-time stochastic neural networks systems with time-varying delays
Applied Mathematics and Computation
Global robust exponential stability of discrete-time interval BAM neural networks with time-varying delays
Applied Mathematical Modelling
Robust stability analysis of static neural network with S-type distributed delays
Applied Mathematical Modelling
New delay-dependent robust stability criterion for uncertain neural networks with time-varying delays
Applied Mathematics and Computation
On improved delay-dependent criterion for global stability of bidirectional associative memory neural networks with time-varying delays
Applied Mathematics and Computation
Robust exponential stability for uncertain stochastic neural networks with discrete and distributed time-varying delays
Physics Letters A
Dynamical behaviors of discrete-time fuzzy cellular neural networks with variable delays and impulses
Journal of the Franklin Institute
Passivity-based control for Hopfield neural networks using convex representation
Applied Mathematics and Computation
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