Delay-dependent Passivity Conditions Research Articles

Passivity analysis of memristor-based impulsive inertial neural networks with time-varying delays

This paper focuses on delay-dependent passivity analysis for a class of memristive impulsive inertial neural networks with time-varying delays. By choosing proper variable transformation, the memristive inertial neural networks can be rewritten as first-order differential equations. The memristive model presented here is regarded as a switching system rather than employing the theory of differential inclusion and set-value map. Based on matrix inequality and Lyapunov-Krasovskii functional method, several delay-dependent passivity conditions are obtained to ascertain the passivity of the addressed networks. In addition, the results obtained here contain those on the passivity for the addressed networks without impulse effects as special cases and can also be generalized to other neural networks with more complex pulse interference. Finally, one numerical example is presented to show the validity of the obtained results.

Further results on passivity analysis of delayed neural networks with leakage delay

This paper is concerned with the passivity problem for neural networks with leakage delay and time-varying transmission delay. Using some novel Lyapunov-Krasovskii (L-K) functionals, and combining with the Wirtinger integral inequality, some less conservative delay-dependent passivity conditions are proposed in terms of linear matrix inequalities (LMIs). Different from the existing approaches, the model transformation is abandoned in this paper, and the proposed L-K functionals incorporate the interconnected terms related to both the leakage delay and the time-varying delay. Numerical examples show that the obtained conditions are less conservative.

Relaxed passivity conditions for discrete-time stochastic delayed neural networks

In this paper, the passivity problem is researched for discrete-time stochastic neural networks with time-varying delay. By utilizing a novel Lyapunov–Krasovskii functional, delay-decomposition method and reciprocally convex approach, some sufficient delay-dependent passivity conditions are established in the form of linear matrix inequalities. Furthermore, these new criteria do not require all the symmetric matrices involved in the employed Lyapunov–Krasovskii functional to be positive definite. Finally, three numerical examples are given to illustrate the reduced conservatism and effectiveness of the proposed method.

Delay-dependent passivity analysis of impulsive neural networks with time-varying delays

This paper investigates delay-dependent passivity for a class of impulsive neural networks with bounded or unbounded time-varying delays. By applying Lyapunov–Krasovskii functional and matrix inequality approach, some new delay-dependent passivity conditions are proposed in terms of the full use of the conditions of neuron activation functions and involved time-varying delays. These passivity conditions are presented in accordance with matrix inequalities, which can be easily verified via standard numerical software. Meanwhile, the results derived here include the existing relative results on the passivity for neural networks without impulse effects as special cases and can also be extended to other neural networks with more complex impulse disturbance. Finally, two numerical examples with simulations are given to demonstrate the effectiveness of the proposed criteria.

New Results on Passivity for Discrete-Time Stochastic Neural Networks with Time-Varying Delays

The problem of passivity analysis for discrete-time stochastic neural networks with time-varying delays is investigated in this paper. New delay-dependent passivity conditions are obtained in terms of linear matrix inequalities. Less conservative conditions are obtained by using integral inequalities to aid in the achievement of criteria ensuring the positiveness of the Lyapunov-Krasovskii functional. At last, numerical examples are given to show the effectiveness 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.

Passivity Analysis of Markovian Jumping Neural Networks with Leakage Time-Varying Delays

This paper is concerned with the passivity analysis of Markovian jumping neural networks with leakage time-varying delays. Based on a Lyapunov functional that accounts for the mixed time delays, a leakage delay-dependent passivity conditions are derived in terms of linear matrix inequalities (LMIs). The mixed delays includes leakage time-varying delays, discrete time-varying delays, and distributed time-varying delays. By employing a novel Lyapunov-Krasovskii functional having triple-integral terms, new passivity leakage delay-dependent criteria are established to guarantee the passivity performance. This performance not only depends on the upper bound of the time-varying leakage delay but also depends on the upper bound of the derivative of the time-varying leakage delay . While estimating the upper bound of derivative of the Lyapunov-Krasovskii functional, the discrete and distributed delays should be treated so as to appropriately develop less conservative results. Two numerical examples are given to show the validity and potential of the developed criteria.

New passivity conditions with fewer slack variables for uncertain neural networks with mixed delays

This paper introduces an effective approach to studying the passivity of neutral-type neural networks with discrete and continuous distributed time-varying delays. By employing a novel Lyapunov–Krasovskii functional based on delay partitioning, several improved delay-dependent passivity conditions are established to guarantee the passivity of uncertain neural networks by applying the Jensen integral inequality. These criteria are expressed in the framework of linear matrix inequalities, which can be verified easily by means of standard Matlab software. One special case of the obtained criteria turns out to be equivalent to some existing result with same reduced conservatism but including fewer slack variables. As the present passivity conditions involve fewer free-weighting matrices, the computational burden is largely reduced. Three examples are provided to demonstrate the advantage of the theoretical results.

Delay-dependent passivity for singular Markov jump systems with time-delays

In this paper, the problem of delay-dependent passivity analysis is studied for the singular Markov jump systems with time-varying/time-invariant delays. By use of the delay partitioning method, two delay-dependent passivity conditions are derived for the considered systems via two novel Lyapunov functionals including mode-dependent double integral terms. Some stochastic stability criteria are also given. All the results reported in this paper not only depend upon the time-delays, but also depend upon their partitioning, which aims at reducing the conservatism. Four numerical examples are proposed to show that the methods proposed here are less conservative than the existing ones thanks to the usage of the delay partitioning method and novel Lyapunov functionals.

Passivity analysis of Markov jump neural networks with mixed time-delays and piecewise-constant transition rates

In this paper, passivity analysis is considered for Markov jump neural networks with both mixed time-delays and time-varying transition rates. The mixed time-delays consist of both discrete and distributed delays. The time-varying character of transition rates is assumed to be piecewise-constant. By use of the linear matrix inequality (LMI) method and a Lyapunov functional that accounts for the mixed time-delays, a delay-dependent passivity condition is derived, which can be easily checked. The result presented depends upon not only discrete delay but also distributed delay. A numerical example is proposed to show the effectiveness of the proposed method.

Robust passivity analysis of a class of discrete-time stochastic neural networks

This paper addresses the passivity problem of a class of discrete-time stochastic neural networks with time-varying delays and norm-bounded parameter uncertainties. New delay-dependent passivity conditions are obtained by using a novel Lyapunov functional together with the linear matrix inequality approach. Numerical examples show the effectiveness of the proposed method.

Passivity-based control for uncertain stochastic jumping systems with mode-dependent round-trip time delays

This paper considers the passivity-based control problem for stochastic jumping systems with mode-dependent round-trip time-varying delays and norm-bounded parametric uncertainties. By utilizing a novel Markovian switching Lyapunov functional, a delay-dependent passivity condition is obtained. Then, based on the derived passivity condition, a desired Markovian switching dynamic output feedback controller is designed, which ensures the resulting closed-loop system is passive. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed results.

Passivity Analysis for Discrete-Time Stochastic Markovian Jump Neural Networks With Mixed Time Delays

In this paper, passivity analysis is conducted for discrete-time stochastic neural networks with both Markovian jumping parameters and mixed time delays. The mixed time delays consist of both discrete and distributed delays. The Markov chain in the underlying neural networks is finite piecewise homogeneous. By introducing a Lyapunov functional that accounts for the mixed time delays, a delay-dependent passivity condition is derived in terms of the linear matrix inequality approach. The case of Markov chain with partially unknown transition probabilities is also considered. All the results presented depend upon not only discrete delay but also distributed delay. A numerical example is included to demonstrate the effectiveness of the proposed methods.

Global robust passivity analysis for stochastic fuzzy interval neural networks with time-varying delays

In this paper, the problem of passivity analysis is investigated for uncertain stochastic fuzzy interval neural networks with time-varying delays. The parameter uncertainties are assumed to be bounded in given compact sets. For the neural networks under study, a generalized activation function is considered, where the traditional assumptions on the boundedness, monotony and differentiability of the activation functions are removed. By constructing proper Lyapunov–Krasovskii functional and employing a combination of the free-weighting matrix method and stochastic analysis technique, new delay-dependent passivity conditions are derived in terms of linear matrix inequalities (LMIs), which can be solved by some standard numerical packages. Finally, numerical examples are given to show the effectiveness and merits of the proposed method.

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.

Robust passivity analysis for Takagi–Sugeno fuzzy stochastic Cohen–Grossberg interval neural networks with time-varying delays

In this paper, the problem of passivity analysis is investigated for uncertain stochastic Cohen–Grossberg fuzzy interval neural networks with time-varying delays. Two types of uncertainties, time-varying structured uncertainty and interval uncertainty, are considered. By constructing proper Lyapunov–Krasovskii functionals and utilizing the stochastic analysis technique, some delay-dependent passivity conditions are derived to ensure the passivity of the concerned neural networks. The proposed results can be expressed in terms of linear matrix inequalities, which can be solved by some standard numerical packages. Finally, numerical examples are given to show the effectiveness and merits 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.

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 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.

Passivity analysis of discrete-time stochastic neural networks with time-varying delays

In this paper, the problem of passivity analysis is investigated for a class of discrete-time stochastic neural networks with time-varying delays. For the neural networks under study, a generalized activation function is considered, where the traditional assumptions on the boundedness, monotony and differentiability of the activation functions are removed. By constructing proper Lyapunov–Krasovskii functional and employing a combination of the free-weighting matrix method and stochastic analysis technique, a delay-dependent passivity condition is derived in terms of linear matrix inequalities (LMIs). Furthermore, when the parameter uncertainties appear in the discrete-time stochastic neural networks with time-varying delays, a delay-dependent robust passivity condition is also presented. An example is given to show the effectiveness of the proposed criterion.