The problem of passivity analysis for a class of discrete-time stochastic neural networks (DSNNs) with time-varying interval delay is investigated. The delay-dependent sufficient criteria are derived in terms of linear matrix inequalities (LMIs). The results are shown to be generalization of some previous results and are less conservative than the existing works. Meanwhile, the computational complexity of the obtained stability conditions is reduced because less variables are involved. Two numerical examples are given to show the effectiveness and the benefits of the proposed method.

Over the past decades, Neural Networks (NNs) have attracted considerable attention because of their extensive applications in pattern recognition, optimization solvers, model identification, signal processing, and other engineering areas [

Most NNs studied are assumed to act in a continuous-time manner; however, in implementing and applications of neural networks, discrete-time neural networks become more and more important than their continuous-time counterparts [

On the other hand, the passivity theory plays an important role in the analysis and design of linear and nonlinear delayed systems. Recently, the passivity of linear systems with delays [

In this paper, by constructing a new Lyapunov-Krasovskii functional, the improved delay-dependent passivity and robust passivity criteria of DSNNs are obtained in the form of linear matrix inequalities (LMIs). It is shown that the obtained conditions are less conservative and more efficiency than those in [

Throughout this paper,

Consider the uncertain DSNNs with time-varying interval delay described by

The initial condition of system (

The activation functions in (

Activation functions

As pointed out in [

The delayed DSNNs (

The purpose of this paper is to find the maximum allowed delay bound

In obtaining the main results of this paper, the following lemma will be useful for the proofs.

Given constant matrices

Given matrices

In this section, we present a delay-dependent criterion guaranteeing the passivity of DSNNs with time-varying delay:

Under Assumption

Choose a new Lyapunov-Krasovskii functional candidate as follows:

Defining

On the other hand, using (

In Theorem

Since the activation functions satisfy Assumption

Given two scalars

Next, we provide the delay-dependent robust passivity analysis for uncertain DSNN (

Given two scalars

Assume that inequality (

We now consider the DSNNs without stochastic term. In this case, the system (

Given two scalars

This section presents two numerical examples that demonstrate the validity of the method described above.

Consider a delayed DSNNs (

The activation functions satisfy Assumption

From Tables

Comparisons of allowable upper bound (

Methods | |||||
---|---|---|---|---|---|

By [ | 48 | 50 | 57 | 67 | |

By Corollary | 48 | 50 | 57 | 67 |

Comparisons of allowable upper bound (

By [ | 7 | 9 | 16 | 26 | |

By Corollary | 7 | 9 | 16 | 26 | |

By Theorem | 8 | 10 | 17 | 27 |

Consider a delayed uncertain DSNNs (

If the time-varying delays satisfy

In this paper, we have considered the problem of passivity and robust passivity analysis for a class of DSNNs with time-varying delay. By choosing a new Lyapunov-Krasovskii functional, the improved delay-dependent criteria have been proposed. Finally, two numerical examples have been provided to illustrate the effectiveness of the obtained results.

This work is partially supported by the Natural Science Foundation of China (60874030, 60835001, 60574006), the Qing Lan Project by the Jiangsu Higher Education Institutions of China, and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant no. 07KJB510125, 08KJD510008, 09KJB510018).