Class Of Uncertain Neural Networks Research Articles

Exponential H∞ stabilization of uncertain neural networks with time-varying delay and external disturbance via periodically intermittent control

This paper is concerned with the exponential [Formula: see text] stabilization for a class of uncertain neural networks with interval time-varying delay and external disturbance via periodically intermittent control. By constructing a novel Lyapunov–Krasovskii functional (LKF) and applying some inequality techniques, delay-dependent sufficient conditions are derived to guarantee the exponential [Formula: see text] stabilization of the considered closed-loop system. These conditions are given in the form of linear matrix inequalities (LMIs). The intermittent state-feedback controller can reduce the effect of external disturbance to a prescribed attenuation level [Formula: see text]. Furthermore, the desired controller gain matrix can be obtained by solving the obtained LMIs. Finally, numerical simulations are given to show the effectiveness and the benefits of the proposed method.

Robust passivity analysis for uncertain neural networks with discrete and distributed time-varying delays

In this paper, we address robust passivity analysis for a class of uncertain neural networks (NNs) with discrete and distributed time-varying delays. By selecting an improved Lyapunov-Krasovskii functional (LKF) with a novel delay-produce-type (DPT) term and combing free-matrix-based (FMB) integral inequality, some sufficient criteria are obtained to guarantee the passivity of uncertain NNs. Then, the maximal allowable upper bound (MAUB) of time-varying delay can be obtained by reciprocally convex combination (RCC) technique through solving a group of linear matrix inequalities (LMIs). Finally, numerical examples are considered to illustrate the benefit and superiority of the method proposed.

Finite-time stabilization of uncertain neural networks with distributed time-varying delays

In this paper, the problem of finite-time stabilization for a class of uncertain neural networks with distributed time-varying delays is investigated. Based on the Lyapunov stability theory and integral inequality technique, some sufficient LMI conditions are derived to ensure the finite-time stability of considered neural networks. In addition, the upper bound of the settling time for stabilization is estimated. Numerical simulations are carried out to demonstrate the effectiveness of the obtained results.

Global exponential stability of uncertain neural networks with discontinuous Lurie-type activation and mixed delays

This paper deals with the problem of the global exponential stability of a class of uncertain neural networks with discontinuous Lurie-type activation and mixed delays. By establishing a new sufficient condition, we first prove the existence of the equilibrium point by using the Leray–Schauder alternative theorem. Then, by employing a new Lyapunov functional, we obtain the global exponential stability of the equilibrium point of the uncertain neural network. In the end, some comparisons and numerical examples are given to show the improvement of the conclusions in this paper.

Less conservative delay-dependent [formula omitted] control of uncertain neural networks with discrete interval and distributed time-varying delays

This paper deals with the robust H∞ control problem for a class of uncertain neural networks with discrete interval and distributed time-varying delays. The main purpose of this paper is to estimate robust asymptotic stability of the given neural network with H∞ performance analysis γ. By constructing novel Lyapunov–Krasovskii functionals with triple integral terms, several new less conservative delay-dependent stability conditions for H∞ control are obtained in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the proposed theoretical results. The method given in this paper shows less conservative results when comparing with some existing methods.

Delay-dependent stability criteria of uncertain Markovian jump neural networks with discrete interval and distributed time-varying delays

In this paper, a class of uncertain neural networks with discrete interval and distributed time-varying delays and Markovian jumping parameters (MJPs) are carried out. The Markovian jumping parameters are modeled as a continuous-time, finite-state Markov chain. By using the Lyapunov–Krasovskii functionals (LKFs) and linear matrix inequality technique, some new delay-dependent criteria is derived to guarantee the mean-square asymptotic stability of the equilibrium point. Numerical simulations are given to demonstrate the effectiveness of the proposed method. The results are also compared with the existing results to show the less conservativeness.

Robust Stabilization andH∞Control for Uncertain Neural Networks with Mixed Time Delays

This paper is concerned with the problem of robust stabilization andH∞control for a class of uncertain neural networks. For the robust stabilization problem, sufficient conditions are derived based on the quadratic convex combination property together with Lyapunov stability theory. The feedback controller we design ensures the robust stability of uncertain neural networks with mixed time delays. We further design a robustH∞controller which guarantees the robust stability of the uncertain neural networks with a givenH∞performance level. The delay-dependent criteria are derived in terms of LMI (linear matrix inequality). Finally, numerical examples are provided to show the effectiveness of the obtained results.

New Results on Passivity Analysis for Uncertain Neural Networks with Time-Varying Delay

The paper investigates the stability and passivity analysis problems for a class of uncertain neural networks with time-delay via delta operator approach. Both the parameter uncertainty and the generalized activation functions are considered in this paper. By constructing an appropriate Lyapunov-Krasovskii functional, some new stability and passivity conditions are obtained in terms of linear matrix inequalities (LMIs). The main characteristic of this paper is to obtain novel stability and passivity analysis criteria for uncertain neural networks with time-delay in the delta operator system framework. A numerical example is presented to demonstrate the effectiveness of the proposed results.

Delay-dependent robust stabilization and H∞ control for neural networks with various activation functions

This paper considers the problem of robust stabilization for a class of uncertain neural networks with various activation functions and mixed time delays. The aim is to derive a H∞ control law to ensure the robust stability of the closed-loop system about its equilibrium with parameter uncertainties. By employing the Lyapunov stability theory and the matrix inequality technique, a new set of sufficient conditions is presented for the existence of the H∞ control problem. The stability criteria are derived in terms of linear matrix inequalities (LMIs) which can be solved easily by the Matlab LMI toolbox. In addition to the requirement of global robust stabilization, for a prescribed H∞ performance level the stabilizing controller gain matrices for all delays to satisfy the upper bound of the time-varying delay are required to be obtained. Numerical examples are presented to illustrate the effectiveness of the proposed method.

Stability analysis for discrete delayed Markovian jumping neural networks with partly unknown transition probabilities

This paper addresses the analysis problem of asymptotic stability for a class of uncertain neural networks with Markovian jumping parameters and time delays. The considered transition probabilities are assumed to be partially unknown. The parameter uncertainties are considered to be norm-bounded. A sufficient condition for the stability of the addressed neural networks is derived, which is expressed in terms of a set of linear matrix inequalities. A numerical example is given to verify the effectiveness of the developed results.

Passivity of uncertain neural networks with both leakage delay and time-varying delay

In this paper, the passivity problem is investigated for a class of uncertain neural networks with leakage delay and time-varying delay as well as generalized activation functions. By constructing appropriate Lyapunov–Krasovskii functionals, and employing Newton–Leibniz formulation and the free-weighting matrix method, several delay-dependent criteria for checking the passivity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Two examples with simulations are given to show the effectiveness and less conservatism of the proposed criteria.

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.

New results on passivity analysis of uncertain neural networks with time-varying delays

In this paper, the passivity problem is investigated for a class of uncertain neural networks with generalized activation functions. By employing an appropriate Lyapunov–Krasovskii functional, 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. An example is 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.

Robust decentralized adaptive control for a class of uncertain neural networks with time-varying delays

This paper considers the robust control problem for a class of uncertain time-varying delayed neural networks, in which the activation function may be a discontinuous function. A robust decentralized adaptive sliding mode controller is proposed to guarantee the asymptotically stability of the system. The proposed controller, which does not dependent on the time delay, ensures the occurrence of the sliding manifold even when the system is undergoing parameter uncertainties and nonlinear input. Two numerical examples are given to show the effectiveness of the proposed controller.

New Globally Asymptotic Stability Criteria for Delayed Cellular Neural Networks

This brief is concerned with the stability analysis for cellular neural networks with time-varying delays. First, an appropriate Lyapunov-Krasovskii functional is introduced to form some new delay-dependent stability conditions in terms of linear matrix inequalities (LMIs). Quite differently, these stability criteria are derived by using the convex combination property, which equivalently converts the original LMI containing a convex combination on the time-varying delay into two boundary LMIs. Second, this newly proposed approach is then extended to a class of uncertain neural networks with time-varying delays, from which new delay-dependent robust stability criteria are formulated. Finally, two numerical examples are given to show that the proposed criteria are of much less conservatism than the existing ones in the literature.

Robust State Estimation for Uncertain Neural Networks With Time-Varying Delay

The robust state estimation problem for a class of uncertain neural networks with time-varying delay is studied in this paper. The parameter uncertainties are assumed to be norm bounded. Based on a new bounding technique, a sufficient condition is presented to guarantee the existence of the desired state estimator for the uncertain delayed neural networks. The criterion is dependent on the size of the time-varying delay and on the size of the time derivative of the time-varying delay. It is shown that the design of the robust state estimator for such neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. Finally, two simulation examples are given to demonstrate the effectiveness of the developed approach.

Global robust stability of neural networks with multiple discrete delays and distributed delays

The problem of global robust stability is investigated for a class of uncertain neural networks with both multiple discrete time-varying delays and distributed time-varying delays. The uncertainties are assumed to be of norm-bounded form and the activation functions are supposed to be bounded and globally Lipschitz continuous. Based on the Lyapunov stability theory and linear matrix inequality technique, some robust stability conditions guaranteeing the global robust convergence of the equilibrium point are derived. The proposed LMI-based criteria are computationally efficient as they can be easily checked by using recently developed algorithms in solving LMIs. Two examples are given to show the effectiveness of the proposed results.

LMI approach to the global robust stability of a larger class of neural networks with delay

Sufficient conditions in the form of linear matrix inequality for the uniqueness and global asymptotic stability of the equilibrium point of a large class of uncertain neural networks with delay are presented. The conditions are based on norm-bounded uncertainties. An example is given to show the effectiveness of the obtained results. A comparison is made between the present approach and an earlier approach due to Lu, Rong and Chen. An error is corrected in an earlier publication.