Passivity Analysis Of Neural Networks Research Articles

Hierarchical Passivity Criterion for Delayed Neural Networks via A General Delay-Product-Type Lyapunov-Krasovskii Functional.

This article is concerned with passivity analysis of neural networks with a time-varying delay. Several techniques in the domain are improved to establish the new passivity criterion with less conservatism. First, a Lyapunov-Krasovskii functional (LKF) is constructed with two general delay-product-type terms which contain any chosen degree of polynomials in time-varying delay. Second, a general convexity lemma without conservatism is developed to address the positive-definiteness of the LKF and the negative-definiteness of its time-derivative. Then, with these improved results, a hierarchical passivity criterion of less conservatism is obtained for neural networks with a time-varying delay, whose size and conservatism vary with the maximal degree of the time-varying delay polynomial in the LKF. It is shown that the conservatism of the passivity criterion does not always reduce as the degree of the time-varying delay polynomial increases. Finally, a numerical example is given to illustrate the proposed criterion and benchmark against the existing results.

Robust passivity analysis of mixed delayed neural networks with interval nondifferentiable time-varying delay based on multiple integral approach

<abstract><p>New results on robust passivity analysis of neural networks with interval nondifferentiable and distributed time-varying delays are investigated. It is assumed that the parameter uncertainties are norm-bounded. By construction an appropriate Lyapunov-Krasovskii containing single, double, triple and quadruple integrals, which fully utilize information of the neuron activation function and use refined Jensen's inequality for checking the passivity of the addressed neural networks are established in linear matrix inequalities (LMIs). This result is less conservative than the existing results in literature. It can be checked numerically using the effective LMI toolbox in MATLAB. Three numerical examples are provided to demonstrate the effectiveness and the merits of the proposed methods.</p></abstract>

Dissipativity and Passivity analysis of neural networks with mixed-time-varying delays

This paper focuses on the problem of Dissipativity and Passivity analysis of NNs with mixed-time-varying delays. By employing Lyapunov functional approach, some sufficient conditions are derived to guarantee that the considered NNs are strictly (Q, S, R)−γ-Dissipative and Passivity. Based on Lyapunov stability theory, proper Lyapunov-Krasovskii functional (LKF) with some new terms is constructed, and estimating their derivative by using newlyndeveloped single integral inequality that includes Jensens inequality which can be easily checked by applying MATLAB LMT toolkit. Three Numerical example is finally provided to demonstrate the effectiveness and advantages of the proposed method.

Auxiliary function-based integral inequality approach to robust passivity analysis of neural networks with interval time-varying delay

Abstract In this paper, we study the problem of passivity for uncertain neural networks with interval time-varying delay. Firstly, a suitable augmented Lyapunov–Krasovskii functional (LKF) containing two triple integral terms is constructed and an auxiliary function-based integral inequality (AFBI) is used to manipulate the augmented single integral terms in the derivative of LKF. Secondly, a special form of the AFBI is applied to deal with the delay-product-type term, which was used to be ignored in the time derivative of a triple integral term. As a result, less conservative delay-dependent passivity criteria are derived for normal delayed neural networks (DNNs) in the form of linear matrix inequalities (LMIs). In addition, with the same LKF, delay-dependent passivity criteria are obtained for normal DNNs without the delay-product-type term. Subsequently, these criteria are extended to DNNs with parameter uncertainties. Finally, four numerical examples and simulations are provided to illustrate the effectiveness of the proposed criteria.

Passivity analysis of neural networks with two different Markovian jumping parameters and mixed time delays

This paper studies the problem of passivity analysis for neural networks with two different Markovian jumping parameters and mixed time delays utilizing some integral inequalities. The integral inequalities produce sharper bounds than what the Jensen's inequality produces, consequently, better results are obtained. The Markovian jumping parameters in connection weight matrices and discrete delay are assumed to be different in the system model. By constructing a new appropriate Lyapunov-Krasovskii functional (LKF), some sufficient conditions are established which guarantee the passivity of the proposed model. Numerical examples are given to show the less conservatism and effectiveness of the proposed method.

New inequality-based approach to passivity analysis of neural networks with interval time-varying delay

This paper is concerned with the problem of passivity analysis of neural networks with an interval time-varying delay. Unlike existing results in the literature, the time-delay considered in this paper is subjected to interval time-varying without any restriction on the rate of change. Based on novel refined Jensen inequalities and by constructing an improved Lyapunov–Krasovskii functional (LKF), which fully utilizes information of the neuron activation functions, new delay-dependent conditions that ensure the passivity of the network are derived in terms of tractable linear matrix inequalities (LMIs) which can be effectively solved by various computational tools. The effectiveness and improvement over existing results of the proposed method in this paper are illustrated through numerical examples.

Improved passivity analysis for neural networks with Markovian jumping parameters and interval time-varying delays

The problem of passivity analysis for neural networks with Markovian jumping parameters and interval time-varying delays is investigated in this paper. By constructing a novel Lyapunov–Krasovskii functional based on the complete delay-decomposing idea and using reciprocally convex technique, some improved delay-dependent passivity criteria are established in terms of linear matrix inequalities. Numerical examples are also given to show the effectiveness of the proposed methods.

Robust passivity analysis of neural networks with discrete and distributed delays

This paper focuses on the problem of passivity of neural networks in the presence of discrete and distributed delay. By constructing an augmented Lyapunov functional and combining a new integral inequality with the reciprocally convex approach to estimate the derivative of the Lyapunov-Krasovskii functional, sufficient conditions are established to ensure the passivity of the considered neural networks, in which some useful information on the neuron activation function ignored in the existing literature is taken into account. Three numerical examples are provided to demonstrate the effectiveness and the merits of the proposed method.

Relaxed passivity conditions for neural networks with time-varying delays

This paper revisits the problem of passivity analysis for neural networks with time-varying delays. A new delay-dependent criterion is obtained in terms of linear matrix inequalities, guaranteeing that the input and output of the considered neural network satisfy a prescribed passivity-inequality constraint. This newly presented criterion does not require all the symmetric matrices involved in the employed quadratic Lyapunov–Krasovskii functional to be positive definite. This feature is remarkable since it sheds new light on the traditional ideas for constructing Lyapunov–Krasovskii functionals. More importantly, the conservatism of delay-dependent passivity conditions can be reduced due to the relaxation on the positive-definiteness of every Lyapunov matrix. It is shown both theoretically and numerically that the passivity criterion proposed in this paper is truly less conservative than some of the latest results in the literature.

Analysis on Passivity for Uncertain Neural Networks with Time-Varying Delays

The problem of passivity analysis for neural networks with time-varying delays and parameter uncertainties is considered. By the consideration of newly constructed Lyapunov-Krasovskii functionals, improved sufficient conditions to guarantee the passivity of the concerned networks are proposed with the framework of linear matrix inequalities (LMIs), which can be solved easily by various efficient convex optimization algorithms. The enhancement of the feasible region of the proposed criteria is shown via two numerical examples by the comparison of maximum allowable delay bounds.

시변 지연을 가진 불확실 뉴럴 네트워크에 대한 지연의존 강인 수동성

In this paper, the problem of passivity analysis for neural networks with time-varying delays and norm-bounded parameter uncertainties is considered. By constructing a new augmented Lyapunov functional, a new delay-dependent passivity criterion for the network is established in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Two numerical example are included to show the effectiveness of proposed criterion.

Passivity analysis for neural networks of neutral type with Markovian jumping parameters and time delay in the leakage term

In this paper, the problem of passivity analysis is investigated for neutral type neural networks with Markovian jumping parameters and time delay in the leakage term. 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. By constructing proper Lyapunov–Krasovskii functional, new delay-dependent passivity conditions are derived in terms of linear matrix inequalities (LMIs). Moreover, it is well known that the passivity behavior of neural networks is very sensitive to the time delay in the leakage term. Finally, three numerical examples are given to show the effectiveness and less conservatism of the proposed method.

Passivity analysis for neural networks with a time-varying delay

This paper deals with the problem of passivity analysis for neural networks with both time-varying delay and norm-bounded parameter uncertainties by employing an improved free-weighting matrix approach. Some useful terms have been retained, which were used to be ignored in the derivative of Lyapunov–Krasovskii functional. Furthermore, the relationship among the time-varying delay, its upper bound and their difference is taken into account. As a result, for two types of time-varying delays, less conservative delay-dependent passivity conditions are obtained in terms of linear matrix inequalities (LMIs), respectively. Finally, a numerical example is given to demonstrate the effectiveness of the proposed techniques.

New Passivity Analysis for Neural Networks With Discrete and Distributed Delays

In this brief, the problem of passivity analysis is investigated for a class of uncertain neural networks (NNs) with both discrete and distributed time-varying delays. By constructing a novel Lyapunov functional and utilizing some advanced techniques, new delay-dependent passivity criteria are established to guarantee the passivity performance of NNs. Essentially different from the available results, when estimating the upper bound of the derivative of Lyapunov functionals, we consider and best utilize the additional useful terms about the distributed delays, which leads to less conservative results. These criteria are expressed in the form of convex optimization problems, which can be efficiently solved via standard numerical software. Numerical examples are provided to illustrate the effectiveness and less conservatism of the proposed results.

Passivity analysis of neural networks with Markovian jumping parameters and interval time-varying delays

In this paper, the problem of passivity analysis is investigated for neural networks with Markovian jumping parameters, interval time-varying delays and norm bounded parameter uncertainties. The delay-dependent passivity conditions are derived for two types of interval time-varying delay in terms of linear matrix inequalities (LMIs). Finally, three numerical examples are given to show the effectiveness of the proposed conditions.

Passivity analysis of neural networks with discrete and distributed delays

In this paper, the passivity problem is investigated for a class of neural networks with discrete and distributed delays as well as generalised activation functions. By constructing proper Lyapunov-Krasovskii functional and employing a combination of the free-weighting matrix method and inequality technique, a new delay-dependent criterion for the passivity of the addressed neural networks is established in terms of Linear Matrix Inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Two examples are given to show the effectiveness and less conservatism of the proposed criterion. It is noteworthy that the traditional assumptions on the differentiability of the time-varying delays and the boundedness of its derivative are removed.

Passivity Analysis of Neural Networks With Time-Varying Delays

This brief considers the problem of passivity analysis for neural networks with both time-varying delays and norm-bounded parameter uncertainties. For two types of time-varying delays, delay-dependent passivity conditions are derived, respectively. These conditions are expressed in terms of linear matrix inequalities. An example is provided to show the less conservatism of the proposed conditions.

A Delay-Dependent Approach to Passivity Analysis for Uncertain Neural Networks with Time-varying Delay

This paper deals with the problem of passivity analysis for neural networks with time-varying delay, which is subject to norm-bounded time-varying parameter uncertainties. The activation functions are supposed to be bounded and globally Lipschitz continuous. Delay-dependent passivity condition is proposed by using the free-weighting matrix approach. These passivity conditions are obtained in terms of linear matrix inequalities, which can be investigated easily by using standard algorithms. Two illustrative examples are provided to demonstrate the effectiveness of the proposed criteria.

Passivity analysis of neural networks with time delay

The passivity conditions for delayed neural networks (DNNs) are considered in this paper. We firstly derive the passivity condition for DNNs without uncertainties, and then extend the result to the case with time-varying parametric uncertainties. The proposed approach is based on a Lyapunov-Krasovskii functional construction. The passivity conditions are presented in terms of linear matrix inequalities, which can be easily solved by using the effective interior-point algorithm. Numerical examples are also given to demonstrate the effectiveness of the theoretical results.