P. Balasubramaniam

Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations

Abstract This paper considers existence, uniqueness and the global asymptotic stability of fuzzy cellular neural networks with mixed delays. The mixed delays include constant delay in the leakage term (i.e., “leakage delay”), time-varying delays and continuously distributed delays. Based on the Lyapunov method and the linear matrix inequality (LMI) approach, some sufficient conditions ensuring global asymptotic stability of the equilibrium point are derived, which are dependent on both the discrete and distributed time delays. These conditions are expressed in terms of LMI and can be easily checked by MATLAB LMI toolbox. In addition, two numerical examples are given to illustrate the feasibility of the result.

Delay-dependent asymptotic stability for stochastic delayed recurrent neural networks with time varying delays ☆

The global asymptotic stability of stochastic recurrent neural networks with time varying delays is analyzed. In this paper, by utilizing the Lyapunov functional and combining with the linear matrix inequality (LMI) approach, we analyze the global asymptotic stability of stochastic delayed recurrent neural networks. In addition, an example is also provided to illustrate the applicability of the result.

Letters: New global exponential stability results for neutral type neural networks with distributed time delays

In this paper, by utilizing the Lyapunov-Krasovkii functional and combining with the linear matrix inequality (LMI) approach, we analyze the global exponential stability of neutral type neural networks with distributed delays. In addition, the examples are provided to illustrate the applicability of the result using LMI control toolbox in MATLAB.

Leakage Delays in T---S Fuzzy Cellular Neural Networks

In this paper, the Takagi–Sugeno (T–S) fuzzy model representation is extended to the stability analysis for cellular neural networks (CNNs) with mixed time-varying delays and time delay in the leakage term via the delay decomposition approach. First, a sufficient condition is given to ensure the existence and uniqueness of equilibrium point by using topological degree theory. Then, we present global asymptotic stability of equilibrium point by using linear matrix inequality (LMI) approach and by constructing an augmented Lyapunov–Krasovskii functional (ALKF) together with convex combination method. The proposed results can be easily solved by some standard numerical packages. Finally, four numerical examples are given to demonstrate the effectiveness and conservativeness of our proposed results.

Global asymptotic stability of BAM fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays

In this article, a class of bidirectional associative memory (BAM) fuzzy cellular neural networks (FCNNs) with time delay in the leakage term, discrete and unbounded distributed delays is formulated to study the global asymptotic stability. This approach is based on the Lyapunov-Krasovskii functional with free-weighting matrices. Using linear matrix inequality (LMI), a new set of stability criteria for BAM FCNNs with time delay in the leakage term, discrete and unbounded distributed delays is obtained. Also, the stability behavior of BAM FCNNs is very sensitive to the time delay in the leakage term. In the absence of a leakage term, a new stability criteria is also derived by employing a Lyapunov-Krasovskii functional and using the LMI approach. Our results establish a new set of stability criteria for BAM FCNNs with discrete and unbounded distributed delays. Numerical examples are provided to illustrate the effectiveness of the developed techniques.

Design of state estimator for neural networks with leakage, discrete and distributed delays ☆

Abstract In this paper, the design problem of state estimator for neural networks with mixed time-varying delays and leakage delays has been investigated. By using appropriate model transformation that shifts the considered systems into the neutral-type time-delay systems, adapting a new Lyapunov–Krasovskii functional which takes into account the range of time-delay, and by making use of some inequality techniques, delay-dependent criteria are developed to estimate the neuron states through available output measurements such that the estimation error system is globally asymptotically stable. The criteria are formulated in terms of a set of linear matrix inequalities (LMIs), which can be checked efficiently by use of some standard numerical packages. Finally, three numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the presented results.

Global robust asymptotic stability analysis of uncertain switched Hopfield neural networks with time delay in the leakage term

This paper deals with the problem of delay-dependent global robust asymptotic stability of uncertain switched Hopfield neural networks (USHNNs) with discrete interval and distributed time-varying delays and time delay in the leakage term. Some Lyapunov––Krasovskii functionals are constructed and the linear matrix inequality (LMI) approach are employed to derive some delay-dependent global robust stability criteria which guarantee the global robust asymptotic stability of the equilibrium point for all admissible parametric uncertainties. The proposed results that do not require the boundedness, differentiability, and monotonicity of the activation functions. Moreover, the stability behavior of USHNNs is very sensitive to the time delay in the leakage term. It can be easily checked via the LMI control toolbox in Matlab. In the absence of leakage delay, the results obtained are also new results. Finally, nine numerical examples are given to show the effectiveness of the proposed results.

Global asymptotic stability of stochastic fuzzy cellular neural networks with multiple time-varying delays

In this paper, the Takagi-Sugeno (T-S) fuzzy model representation is extended to the stability analysis for stochastic cellular neural networks with multiple time-varying delays using linear matrix inequality (LMI) theory. A novel LMI-based stability criterion is derived to guarantee the asymptotic stability of stochastic cellular neural networks with multiple time-varying delays which are represented by T-S fuzzy models. In order to derive delay-dependent stability conditions, free-weighting matrices method has been introduced, which may develop less-conservative results. In fact, these techniques lead to generalized and less-conservative stability condition that guarantee the wide stability region. Our results can be specialized to several cases including those studied extensively in the literature. Finally, numerical examples are given to demonstrate the effectiveness and conservativeness of our results.

LMI conditions for global asymptotic stability results for neutral-type neural networks with distributed time delays

Abstract In this paper, the global asymptotic stability of neutral-type neural networks with unbounded distributed delays is analyzed by utilizing the Lyapunov–Krasovskii functional and the linear matrix inequality (LMI) approach. A new sufficient condition ensuring the global asymptotic stability for neutral-type neural networks is obtained by using the powerful MATLAB LMI toolbox. Two examples are provided to illustrate the applicability of the stability results.

Global asymptotic stability of stochastic BAM neural networks with distributed delays and reaction-diffusion terms

This paper is concerned with global asymptotic stability of a class of reaction-diffusion stochastic Bi-directional Associative Memory (BAM) neural networks with discrete and distributed delays. Based on suitable assumptions, we apply the linear matrix inequality (LMI) method to propose some new sufficient stability conditions for reaction-diffusion stochastic BAM neural networks with discrete and distributed delays. The obtained results are easy to check and improve upon the existing stability results. An example is also given to demonstrate the effectiveness of the obtained results.