R. Rakkiyappan

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.

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.

Delay-interval dependent robust stability criteria for stochastic neural networks with linear fractional uncertainties

In this paper, we study the delay-interval dependent robust stability criteria for stochastic neural networks with linear fractional uncertainties. The time-varying delay is assumed to belong to an interval and is a fast time-varying function. The uncertainty under consideration includes linear fractional norm-bounded uncertainty. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Finally, some numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions.

Delay dependent stability analysis of neutral systems with mixed time-varying delays and nonlinear perturbations

This paper is concerned with the problem of stability of neutral systems with interval time-varying delays and nonlinear perturbations. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties. A new delay-dependent stability condition is derived in terms of linear matrix inequality by constructing a new Lyapunov functional and using some integral inequalities without introducing any free-weighting matrices. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

Global asymptotic stability of stochastic recurrent neural networks with multiple discrete delays and unbounded distributed delays

Abstract In this paper using Lyapunov–Krasovskii functional and the linear matrix inequality (LMI) approach the global asymptotic stability of stochastic recurrent neural networks with multiple discrete time-varying delays and distributed delays is analyzed. A new sufficient condition ensuring the global asymptotic stability for delayed recurrent neural networks is obtained in the stochastic sense using the powerful MATLAB LMI toolbox. Two examples are provided to illustrate the applicability of the stability results.

Delay dependent stability results for fuzzy BAM neural networks with Markovian jumping parameters

This paper deals with the delay-dependent asymptotic stability analysis problem for a class of fuzzy bidirectional associative memory (BAM) neural networks with time-varying interval delays and Markovian jumping parameters by Takagi-Sugeno (T-S) fuzzy model. The nonlinear delayed BAM neural networks are first established as a modified T-S fuzzy model in which the consequent parts are composed of a set of Markovian jumping BAM neural networks with time-varying interval delays. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite-state space. The new type of Markovian jumping matrices Pk and Qk are introduced in this paper. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. A new delay-dependent stability condition is derived in terms of linear matrix inequality by constructing a new Lyapunov-Krasovskii functional and introducing some free-weighting matrices. Numerical examples are given to demonstrate the effectiveness of the proposed methods.

On exponential stability results for fuzzy impulsive neural networks

Complex nonlinear systems can be represented to a set of linear sub-models by using fuzzy sets and fuzzy reasoning via ordinary Takagi-Sugeno (TS) fuzzy models. In this paper, the exponential stability of TS fuzzy neural networks with impulsive effect and time-varying delays is investigated. The model for fuzzy impulsive neural networks with time-varying delays is first established as a modified TS fuzzy model in which the consequent parts are composed of a set of impulsive neural networks with time-varying delays. Secondly, the exponential stability for fuzzy impulsive neural networks is presented by utilizing the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) approach. In addition, two numerical examples are provided to illustrate the applicability of the result using LMI control toolbox in MATLAB.