Delay-dependent Passivity Criterion Research Articles

Robust passivity analysis of uncertain neutral-type neural networks with distributed interval time-varying delay under the effects of leakage delay

This paper deals with the problem of delay-range-dependent robust passivity analysis of uncertain neutral-type neural networks with distributed interval time-varying delay under the effects of leakage delay. The uncertainties under consideration are norm-bounded uncertainties and the restriction on the derivative of the discrete and distributed interval time-varying delays is removed, which means that a fast interval time-varying delay is allowed. By applying a novel Lyapunov-Krasovskii functional approach, improved integral inequalities, Leibniz-Newton formula and utilization of zero equation, then a new delay-range-dependent passivity criterion of neutral-type neural networks with distributed interval time-varying delay under the effects of leakage delay is established in terms of linear matrix inequalities (LMIs). Furthermore, some less conservative delay-dependent passivity criteria are obtained. Moreover, we derived a robust passivity criterion for uncertain neutral-type neural networks with distributed interval time-varying delay under the effects of leakage delay. Besides, a less conservative delay-dependent robust passivity criterion is obtained. Finally, five numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.

Design of Stochastic Passivity and Passification for Delayed BAM Neural Networks with Markov Jump Parameters via Non-uniform Sampled-Data Control

This paper investigates the issue of passivity and passification for delayed Markov jump bidirectional associate memory (BAM)-Type neural networks via non-uniform sampled-data control. By utilizing the Lyapunov–Krasovskii functional strategy, a novel delay-dependent passivity criterion is developed with respect to linear matrix inequalities to guarantee the Markov jump delayed BAM neural frameworks to be passive. At that point, in view of the got passivity conditions, the passification issue is further tackled by planning a mode-dependent non-uniform sampled-data controller design is presented. Finally, a numerical example is provided to illustrate the applicability and effectiveness of the theoretical result.

Passivity Analysis for Quaternion-Valued Memristor-Based Neural Networks With Time-Varying Delay.

This paper is concerned with the problem of global exponential passivity for quaternion-valued memristor-based neural networks (QVMNNs) with time-varying delay. The QVMNNs can be seen as a switched system due to the memristor parameters are switching according to the states of the network. This is the first time that the global exponential passivity of QVMNNs with time-varying delay is investigated. By means of a nondecomposition method and structuring novel Lyapunov functional in form of quaternion self-conjugate matrices, the delay-dependent passivity criteria are derived in the forms of quaternion-valued linear matrix inequalities (LMIs) as well as complex-valued LMIs. Furthermore, the asymptotical stability criteria can be obtained from the proposed passivity criteria. Finally, a numerical example is presented to illustrate the effectiveness of the theoretical results.

Passivity Analysis of Delayed Neural Networks Based on Lyapunov-Krasovskii Functionals With Delay-Dependent Matrices.

This paper is concerned with passivity of a class of delayed neural networks. In order to derive less conservative passivity criteria, two Lyapunov-Krasovskii functionals (LKFs) with delay-dependent matrices are introduced by taking into consideration a second-order Bessel-Legendre inequality. In one LKF, the system state vector is coupled with those vectors inherited from the second-order Bessel-Legendre inequality through delay-dependent matrices, while no such coupling of them exists in the other LKF. These two LKFs are referred to as the coupled LKF and the noncoupled LKF, respectively. A number of delay-dependent passivity criteria are derived by employing a convex approach and a nonconvex approach to deal with the square of the time-varying delay appearing in the derivative of the LKF. Through numerical simulation, it is found that: 1) the coupled LKF is more beneficial than the noncoupled LKF for reducing the conservatism of the obtained passivity criteria and 2) the passivity criteria using the convex approach can deliver larger delay upper bounds than those using the nonconvex approach.

Exponential passivity conditions on neutral stochastic neural networks with leakage delay and partially unknown transition probabilities in Markovian jump

This paper studies the problem of exponential passivity for neutral stochastic neural networks (NSNN) with leakage delay and Markovian jump. The Markovian jump has partially unknown transition probabilities (PUTPs). By utilizing the Itô differential rule, choosing a suitable Lyapunov–Krasovskii functional and combining with the inequality technique, the sufficient delay-dependent exponential passivity criteria are obtained. These sufficient conditions are provided in the form of linear matrix inequalities (LMIs), which can be easily solved by LMI toolbox in Matlab. Finally, two simulated numerical examples are discussed in detail to illustrate the effectiveness of the established results.

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.

Design of passivity and passification for delayed neural networks with Markovian jump parameters via non-uniform sampled-data control

The motivation behind this paper is to explore the issue of passivity and passification for delayed neural networks with Markov jump parameters. A state feedback control approach with non-uniform sampling period is considered. The interest of this paper lies in the thought about another basic uniqueness wound up being less conservatism than watched Jensen’s inequality and takes totally the relationship between the terms in the Leibniz–Newton formula inside the arrangement of linear matrix inequalities. By utilizing the Lyapunov–Krasovskii functional strategy, a novel delay-dependent passivity criterion is developed with respect to linear matrix inequalities to guarantee the Markov jump delayed neural frameworks to be passive. Passivity and passification problems are tackled by using mode-dependent non-uniform sampled-data control. Using many examples from the literature, it is exhibited that the proposed stabilization theorem is less direct than past results. Finally, the framework is associated with benchmark issue, exhibiting to gather compelling stability criteria for reasonable issues, using the proposed strategy.

New Criteria of Passivity Analysis for Fuzzy Time-Delay Systems With Parameter Uncertainties

This paper investigates the passivity problem for a class of uncertain stochastic fuzzy nonlinear systems with mixed delays and nonlinear noise disturbances by employing an improved free-weighting matrix approach. The fuzzy system is based on the Takagi–Sugeno model that is often used to represent the complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning. To reflect more realistic dynamical behaviors of the system, the parameter uncertainties, the stochastic disturbances, and nonlinearities are considered, where the parameter uncertainties enter into all the system matrices, the stochastic disturbances are given in the form of a Brownian motion. The mixed delays comprise both discrete and distributed time-varying delays. By taking the relationship among the time delays, their lower and upper bounds into account, some less conservative linear-matrix-inequality-based delay-dependent passivity criteria are obtained without ignoring any useful terms in the derivative of Lyapunov functional. Finally, numerical examples are given to demonstrate the effectiveness and merits of the proposed methods.

New passivity criteria for memristor-based neutral-type stochastic BAM neural networks with mixed time-varying delays

This paper deals with the problem of passivity analysis issue for a class of memristor-based neutral-type stochastic bidirectional associative memory neural networks (MNSBAMNNs) with discrete interval and distributed time-varying delays. By constructing new Lyapunov–Krasovskii functional (LKF) with quadruple integral terms and suitable activation function conditions, some delay-dependent passivity criteria are obtained in the linear matrix inequality (LMI) format. A numerical example is given to demonstrate the effectiveness and superiority of the new scheme.

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.

Passivity and Passification of Memristor-Based Recurrent Neural Networks With Additive Time-Varying Delays.

This paper presents a new design scheme for the passivity and passification of a class of memristor-based recurrent neural networks (MRNNs) with additive time-varying delays. The predictable assumptions on the boundedness and Lipschitz continuity of activation functions are formulated. The systems considered here are based on a different time-delay model suggested recently, which includes additive time-varying delay components in the state. The connection between the time-varying delay and its upper bound is considered when estimating the upper bound of the derivative of Lyapunov functional. It is recognized that the passivity condition can be expressed in a linear matrix inequality (LMI) format and by using characteristic function method. For state feedback passification, it is verified that it is apathetic to use immediate or delayed state feedback. By constructing a Lyapunov-Krasovskii functional and employing Jensen's inequality and reciprocal convex combination technique together with a tighter estimation of the upper bound of the cross-product terms derived from the derivatives of the Lyapunov functional, less conventional delay-dependent passivity criteria are established in terms of LMIs. Moreover, second-order reciprocally convex approach is employed for deriving the upper bound for terms with inverses of squared convex parameters. The model based on the memristor with additive time-varying delays widens the application scope for the design of neural networks. Finally, pertinent examples are given to show the advantages of the derived passivity criteria and the significant improvement of the theoretical approaches.

Passivity analysis for uncertain discrete-time stochastic BAM neural networks with time-varying delays

This paper is concerned with the passivity analysis problem for a class of discrete-time stochastic bidirectional associative memory neural networks with time-varying delays. Furthermore, the results are extended to the robust passivity analysis with mixed time delays that consist of both the discrete and distributed time delays, and the uncertainties are assumed to be time-varying norm bounded parameter uncertainties. By constructing a new Lyapunov---Krasovskii functional and introducing some appropriate free-weighting matrices, a delay-dependent passivity criterion is derived in terms of LMIs whose feasibility can be easily checked by some available software packages. Finally, two numerical examples with simulation results are given to demonstrate the effectiveness and usefulness of the proposed results.

Passivity and passification for Markov jump genetic regulatory networks with time-varying delays

This paper investigates the problems of passivity and passification for a class of nonlinear Markov jump genetic regulatory networks with time-varying delays and disturbances. By utilizing the Lyapunov–Krasovskii functional method, a novel delay-dependent passivity criterion is established in terms of linear matrix inequalities to guarantee the Markov jump genetic regulatory networks to be passive. Then, based on the obtained passivity conditions, the passification problem is further solved by designing a mode-dependent state feedback controller. A numerical example is presented to demonstrate the effectiveness and validity of the proposed approaches.

State estimation for delayed genetic regulatory networks based on passivity theory

This paper is concerned with the state estimation problem for delayed genetic regulatory networks (GRNs) based on passivity analysis approach. The main purpose of the problem is to design the estimator to approximate the true concentrations of the mRNA and protein through available measurement outputs. Time-varying delays are explicitly assumed to be non-differentiable and constraint on the derivative of the time-varying delay is less than one can be removed. Based on the Lyapunov–Krasovskii functionals involving triple integral terms, using some integral inequalities and convex combination technique, a delay-dependent passivity criterion is established for GRNs in terms of linear matrix inequalities (LMIs) that can efficiently be solved by any available LMI solvers. Finally, numerical examples and simulation are presented to demonstrate the efficiency of the proposed estimation schemes.

Delay-dependent passivity criteria for uncertain switched neural networks of neutral type with interval time-varying delay

This paper is concerned with the robust passivity analysis of uncertain switched neural networks of neutral type with interval time-varying delay. We first discuss the passivity conditions for the addressed model with norm bounded uncertainties and then extend this result to the case of interval uncertainties. For the neural networks under study, a generalized activation function is considered, where the traditional assumptions on the boundedness, monotonicity and differentiability of the activation functions are removed. Constructing a new Lyapunov–Krasovskii functional with triple integral terms and using a minimal number of free-weighting matrices, some passivity criteria are proposed in terms of linear matrix inequalities, which are dependent on the size of the time delay. Finally, some numerical examples are given to illustrate the effectiveness and merits of the developed techniques.

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.

Robust passivity analysis of fuzzy Cohen–Grossberg BAM neural networks with time-varying delays

This paper is concerned with the problem of passivity analysis for a class of Cohen–Grossberg fuzzy bidirectional associative memory (BAM) neural networks with time varying delay. By employing the delay fractioning technique and linear matrix inequality optimization approach, delay dependent passivity criteria are established that guarantees the passivity of fuzzy Cohen–Grossberg BAM neural networks with uncertainties. The passivity condition is expressed in terms of LMIs, which can be easily solved by various convex optimization algorithms. Finally, a numerical example is given to illustrate the effectiveness of the proposed result.

Passivity-based Control for Markovian Jump Systems via Retarded Output Feedback

This paper is concerned with the problem of passivity-based control for Markovian jump systems via retarded output feedback controllers. A delay-dependent passivity criterion is obtained in terms of linear matrix inequalities. Based on this, a sufficient condition is proposed for the design of a retarded output feedback controller which ensures that the closed-loop system is passive. By using the sequential linear programming matrix method, a desired retarded output feedback controller can be constructed. Numerical examples are provided to demonstrate the advantage and effectiveness of the proposed method.

Improved approach for passive stability of discrete-time Markovian jump linear systems via mode-dependent time-delayed controllers

SUMMARY In this paper, we investigate the problem of passive stability for discrete-time Markovian jump linear systems via mode-dependent time-delayed controllers by employing an improved free-weighting matrix approach. A Markov process as discrete-time, discrete-state Markov process is considered. First, a new result of mode-dependent stability analysis is first established for error systems without ignoring any terms in the derivative of Lyapunov–Krasovskii function by considering the relationship between the time-varying delay and its upper bound. Then, the delay-dependent passivity criterion is provided and a mode-dependent time-delayed controller is designed in terms of linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness and less conservativeness of our proposed method. Copyright © 2011 John Wiley & Sons, Ltd.

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.