Additive Time-varying Delay Components Research Articles

Extended dissipative analysis for memristive neural networks with two additive time-varying delay components

This paper concentrates on the extended dissipativity of memristive neural networks with two additive time-varying delays. After giving a foundation to the memristive model, the paper establishes some fundamental results on quadratically stability and extended dissipativity criteria by means of the Lyapunov functional, integral inequality, as well as the relationship between time-varying delays. The novel extended dissipative inequality contains several weighting matrices, by converting the weighting matrices in a new performance index, the extended dissipativity will be degraded to the H∞ performance, L2−L∞ performance, passivity and dissipativity, respectively. Finally, one example is given to substantiate the significant improvement of the theoretical approaches.

State estimation for uncertain Markovian jump neural networks with mixed delays

This paper investigates the problem of state estimation for uncertain Markovian jump neural networks(NNs) with additive time-varying discrete delay components and distributed delay. By constructing a novel Lyapunov–Krasovskii function with multiple integral terms and using an improved inequality, several sufficient conditions are derived. Some improved conditions are formulated in terms of a set of linear matrix inequalities (LMIs), under which the estimation error system is globally exponentially stable in the mean square sense. Some numerical examples are provided to demonstrate the effectiveness of the proposed results.

Improved Stability Criteria for Neural Networks with Additive Time-varying Delay Components

Improved Stability Criteria for Neural Networks with Additive Time-varying Delay Components

New delay-interval-dependent stability analysis of neutral type BAM neural networks with successive time delay components

This paper considers the problem of stability analysis of uncertain neutral type BAM neural networks with two additive time-varying delay components. The relationship between the time-varying delay and its lower and upper bounds is taken into account. Based on the Lyapunov–Krasovskii functional and free-weighting matrix method, delay-dependent sufficient conditions for the solvability of this problem are proposed in terms of LMIs. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed method.

Robust passivity analysis for stochastic impulsive neural networks with leakage and additive time-varying delay components

The purpose of this paper is to investigate the problem of robust passivity analysis for delayed stochastic impulsive neural networks with leakage and additive time-varying delays. The novel contribution of this paper lies in the consideration of a new integral inequality proved to be well-known Jensen’s inequality and takes fully the relationship between the terms in the Leibniz–Newton formula within the framework of linear matrix inequalities (LMIs). By constructing a suitable Lyapunov–Krasovskii functional with triple and four integral terms using Jensen’s inequality, integral inequality technique and LMI frame work, which guarantees stability for the passivity of addressed neural networks. This LMI can be easily solved via convex optimization techniques. Finally, two interesting numerical examples are given to show the effectiveness of the theoretical results.

Synchronization of singular Markovian jumping complex networks with additive time-varying delays via pinning control

This study examines the problem of synchronization for singular complex dynamical networks with Markovian jumping parameters and two additive time-varying delay components. The complex networks consist of m modes which switch from one mode to another according to a Markovian chain with known transition probability. Pinning control strategies are designed to make the singular complex networks synchronized. Based on the appropriate Lyapunov–Krasovskii functional, introducing some free weighting matrices and using convexity of matrix functions, a novel synchronization criterion is derived. The proposed sufficient conditions are established in the form of linear matrix inequalities. Finally, a numerical example is presented to illustrate the effectiveness of the obtained results.

Comments on ‘Improved delay-dependent stability criteria for continuous systems with two additive time-varying delay components’

In this write-up, comments on the omission of few important inequality conditions (or constraints) in the LMI optimization problem stated as delay-dependent stability criterion for a class of linear systems with two additive time-varying state-delays in Cheng et al. (2014) is reported. The omission paves way to incorrectness of the published result. The consequence of the omission, and the revised result are presented in the sequel.

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.

Robust delay-depent stability criteria for uncertain neural networks with two additive time-varying delay components

This paper considers the problem of robust stability of uncertain neural networks with two additive time varying delay components. The activation functions are monotone nondecreasing with known lower and upper bounds. By constructing of a modified augmented Lyapunov function, some new stability criteria are established in terms of linear matrix inequalities, which is easily solved by various convex optimization techniques. Compared with the existing works, the obtained criteria are less conservative due to reciprocal convex technique and an improved inequality, which provides more accurate upper bound than Jensen inequality for dealing with the cross-term. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.

New delay-dependent stability criteria for switched Hopfield neural networks of neutral type with additive time-varying delay components

The objective of this paper is to analyze the stability of switched Hopfield neural networks of neutral type with additive time-varying discrete delay components and finitely distributed delay. By constructing a suitable Lyapunov–Krasovskii functional with triple and four integral terms and by using Finsler׳s lemma, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities to ensure the asymptotic stability of the equilibrium point of the considered neural networks. The derived criteria use the information of the upper delay bounds, which may lead to conservativeness. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.

Stability Criteria for Neural Networks with Two Additive Time-varying Delay Components

This paper is concerned with the stability problem with two additive time-varying delay components. By choosing one augmented Lyapunov-Krasovskii functional, using some new zero equalities, and combining linear matrix inequalities (LMI) techniques, two new sufficient criteria ensuring the global stability asymptotic stability of DNNs is obtained. These stability criteria are present in terms of linear matrix inequalities and can be easily checked. Finally, some examples are showed to demonstrate the effectiveness and less conservatism of the proposed method. Keywords—Neural networks, Globally asymptotic stability, LMI approach, Additive time-varying delays.

Stability Criteria for Neural Networks with Two Additive Time-varying Delay Components

Stability Criteria for Neural Networks with Two Additive Time-varying Delay Components

Stability Criteria for Neural Networks with Two Additive Time-varying Delay Components

Stability Criteria for Neural Networks with Two Additive Time-varying Delay Components

Stability Criteria for Neural Networks with Two Additive Time-varying Delay Components

Stability Criteria for Neural Networks with Two Additive Time-varying Delay Components

Stability Criteria for Neural Networks with Two Additive Time-varying Delay Components

Stability Criteria for Neural Networks with Two Additive Time-varying Delay Components

Stability Criteria for Neural Networks with Two Additive Time-varying Delay Components

Stability Criteria for Neural Networks with Two Additive Time-varying Delay Components

Stability Criteria for Neural Networks with Two Additive Time-varying Delay Components

Stability Criteria for Neural Networks with Two Additive Time-varying Delay Components

Improved delay-dependent stability criteria for continuous system with two additive time-varying delay components

This paper investigated the problem of improved delay-dependent stability criteria for continuous system with two additive time-varying delay components. Free weighting matrices and convex combination method are not involved, which achieves much less numbers of linear matrix inequalities (LMIs) and LMIs scalar decision variables. By taking advantage of integral inequality and new Lyapunov–Krasovskii functional, new less conservative delay-dependent stability criterion is derived. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

New approaches on stability criteria for neural networks with two additive time-varying delay components

In this paper, we study the stability problem for neural networks with two additive time-varying delay components. By constructing the Lyapunov–Krasovskii functional and considering the relationship between time-varying delays and their upper delay bounds, delay-dependent stability criteria are obtained by using reciprocally convex method and convex polyhedron method, respectively. More information of the lower and upper delay bounds of time-varying delays is used to derive the stability criteria, which can lead less conservative results. All the obtained criteria are in terms of Linear Matrix Inequalities (LMIs). Numerical examples are given to show the effectiveness and less conservativeness of the proposed method.

Improved Stability Criteria for Neural Networks with Two Additive Time-Varying Delay Components

In this paper, the stability analysis of neural networks with two additive time-varying delay components is considered. By constructing an augmented Lyapunov–Krasovskii functional, an improved delay-dependent stability criteria are derived by utilizing the delay-partitioning approach, which can effectively deal with the integral terms. As a result, no bounding technique is involved. Two illustrative examples are listed to show the effectiveness of the proposed method.