Delay-dependent state estimation for T-S fuzzy delayed Hopfield neural networks

This paper proposes a new delay-dependent state estimator for Takagi–Sugeno (T-S) fuzzy delayed Hopfield neural networks. By employing a suitable Lyapunov–Krasovskii functional, a delay-dependent criterion is established to estimate the neuron states through available output measurements such that the dynamics of the estimation error is asymptotically stable. It is shown that the design of the proposed 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. An illustrative example is given to demonstrate the effectiveness of the proposed state estimator.     

State estimation of neural networks with time-varying delays and Markovian jumping parameter based on passivity theory

In this paper, the state estimation problem is investigated for neural networks with time-varying delays and Markovian jumping parameter based on passivity theory. The neural networks have a finite number of modes and the modes may jump from one to another according to a Markov chain. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time-delays, the dynamics of the estimation error is globally stable in the mean square and passive from the control input to the output error. Based on the new Lyapunov?CKrasovskii functional and passivity theory, delay-dependent conditions are obtained in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate effectiveness of the proposed method and results.     

State estimator for neural networks with sampled data using discontinuous Lyapunov functional approach

In this paper, the sampled-data state estimation problem is investigated for neural networks with time-varying delays. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled data estimator is constructed. Based on the extended Wirtinger inequality, a discontinuous Lyapunov functional is introduced, which makes full use of the sawtooth structure characteristic of sampling input delay. New delay-dependent criteria are developed to estimate the neuron states through available output measurements such that the estimation error system is asymptotically stable. The criteria are formulated in terms of a set of linear matrix inequalities (LMIs), which can be checked efficiently by use of some standard numerical packages. Finally, a numerical example and its simulations are given to demonstrate the usefulness and effectiveness of the presented results.     

Design of state estimator for uncertain neural networks via the integral-inequality method

The issue of state estimation is studied for a class of neural networks with norm-bounded parameter uncertainties and time-varying delay. Some new linear matrix inequality (LMI) representations of delay-dependent stability criteria are presented for the existence of the desired estimator for all admissible parametric uncertainties. The proposed method is based on the S-procedure and an extended integral inequality which can be deduced from the well-known Leibniz–Newton formula and Moon’s inequality. The results extend some models reported in the literature and improve conservativeness of those in the case that the derivative of the time-varying delay is assumed to be less than one. Two numerical examples are given to show the effectiveness and superiority of the results.     

On improved passivity criteria of uncertain neural networks with time-varying delays

In this paper, the problem of passivity analysis for uncertain neural networks with time-varying delays is considered. By constructing an augmented Lyapunov–Krasovskii’s functional and some novel analysis techniques, improved delay-dependent criteria for checking the passivity of the neural networks are established. The proposed criteria are represented in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Two numerical examples are included to show the superiority of our results.     

State estimation for Markovian jumping recurrent neural networks with interval time-varying delays

The paper is concerned with the state estimation problem for a class of neural networks with Markovian jumping parameters. The neural networks have a finite number of modes and the modes may jump from one to another according to a Markov chain. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time-delays, the dynamics of the estimation error are globally stable in the mean square. A new type of Markovian jumping matrix P _i is introduced in this paper. The discrete 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. Based on the new Lyapunov–Krasovskii functional, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions.     

Exponential state estimation for delayed recurrent neural networks with sampled-data

In this paper, the sampled-data state estimation problem is investigated for a class of recurrent neural networks with time-varying delay. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled-data estimator is constructed. By converting the sampling period into a bounded time-varying delay, the error dynamics of the considered neural network is derived in terms of a dynamic system with two different time-delays. Subsequently, by choosing an appropriate Lyapunov functional and using the Jensen??s inequality, a sufficient condition depending on the sampling period is obtained under which the resulting error system is exponentially stable. Then a sampled-data estimator is designed in terms of the solution to a set of linear matrix inequalities (LMIs) which can be solved by using available software. Finally, a numerical example is employed to demonstrate the effectiveness of the proposed sampled-data estimation approach.     

Passivity analysis for discrete-time switched neural networks with various activation functions and mixed time delays

This paper is concerned with the passivity analysis for a class of discrete-time switched neural networks with various activation functions and mixed time delays. The mixed time delays under consideration include time-varying discrete delay and bounded distributed delay. By using the average dwell time approach and the discontinuous piecewise Lyapunov function technique, a novel delay-dependent sufficient condition for exponential stability of the switched neural networks with passivity is derived in terms of a set of linear matrix inequalities (LMIs). The obtained condition is not only dependent on the discrete delay bound, but also dependent on the distributed delay bound. A numerical example is given to demonstrate the effectiveness of the proposed result.     

Design of sampled data state estimator for Markovian jumping neural networks with leakage time-varying delays and discontinuous Lyapunov functional approach

This paper is concerned with the sampled-data state estimation problem for neural networks with both Markovian jumping parameters and leakage time-varying delays. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled-data estimator is constructed. In order to make full use of the sawtooth structure characteristic of the sampling input delay, a discontinuous Lyapunov functional is proposed based on the extended Wirtinger inequality. A less conservative delay dependent stability criterion is derived via constructing a new triple-integral Lyapunov–Krasovskii functional and the famous Jenson integral inequality. Based on the Lyapunov–Krasovskii functional approach, a state estimator of the considered neural networks has been achieved by solving some linear matrix inequalities, which can be easily facilitated by using the standard numerical software. Finally, two numerical examples are provided to show the effectiveness of the proposed methods.     

Exponential stability for switched Cohen–Grossberg neural networks with average dwell time

In this paper, uncertain switched Cohen–Grossberg neural networks with interval time-varying delay and distributed time-varying delay are proposed. Novel multiple Lyapunov functions are employed to investigate the stability of the switched neural networks under the switching rule with the average dwell time property. Sufficient conditions are obtained in terms of linear matrix inequalities (LMIs) which guarantee the exponential stability for the switched Cohen–Grossberg neural networks. Numerical examples are provided to illustrate the effectiveness of the proposed method.     

State estimation for switched discrete-time stochastic BAM neural networks with time varying delay

This paper focuses the issue of state estimation for a class of switched discrete-time stochastic bidirectional associative memory (BAM) neural networks with time varying delay. The main purpose of this paper is to estimate the neuron states through available output measurements such that the dynamics of the error state system to be robustly exponentially stable. By employing average dwell time approach together with piecewise Lyapunov functional technique, a set of sufficient conditions is derived with respect to all admissible uncertainties, to guarantee the existence of the desired state estimator for the uncertain switched discrete-time BAM delayed neural networks. Specifically, we derive sufficient conditions to achieve robust state estimation with the characterization of complex effects of time delays, parameter uncertainties, and stochastic perturbations. In particular, the parameter uncertainties are assumed to be time varying and unknown, but norm bounded. It should be mentioned that our estimation results are delay dependent, which depend on not only the upper bounds of time delay, but also their lower bounds. More precisely, the desired estimator matrix gain is obtained in terms of the solution of the derived LMIs. Finally, numerical examples with a simulation result are given to illustrate the effectiveness and applicability of the obtained results.     

Synchronization of stochastic chaotic neural networks with reaction-diffusion terms

In this paper, we are concerned with the synchronization problem of a class of stochastic reaction-diffusion neural networks with time-varying delays and Dirichlet boundary conditions. By using the Lyapunov–Krasovskii functional method, feedback control approach and stochastic analysis technology, delay-dependent synchronization conditions including the information of reaction-diffusion terms are presented, which are expressed in terms of linear matrix inequalities (LMIs). The feedback controllers can be constructed by solving the derived LMIs. Finally, illustrative examples are given to show the effectiveness of the proposed technique.     

Passivity analysis of stochastic time-delay neural networks

Passivity analysis of stochastic neural networks with time-varying delays and parametric uncertainties is investigated in this paper. Passivity of stochastic neural networks is defined. Both delay-independent and delay-dependent stochastic passivity conditions are presented in terms of linear matrix inequalities (LMIs). The results are established by using the Lyapunov–Krasovskii functional method. In order to derive the delay-dependent passivity criterion, some free-weighting matrices are introduced. The effectiveness of the method is illustrated by numerical examples.     

Sampled-data state estimation for delayed neural networks with Markovian jumping parameters

This paper is concerned with the sampled-data state estimation problem for a class of delayed neural networks with Markovian jumping parameters. Unlike the classical state estimation problem, in our state estimation scheme, the sampled measurements are adopted to estimate the concerned neuron states. The neural network under consideration is assumed to have multiple modes that switch from one to another according to a given Markovian chain. By utilizing the input delay approach, the sampling period is converted into a time-varying yet bounded delay. Then a sufficient condition is given under which the resulting error dynamics of the neural networks is exponentially stable in the mean square. Based on that, a set of sampled-data estimators is designed in terms of the solution to a set of linear matrix inequalities (LMIs) which can be solved by using the available software. Finally, a numerical example is used to show the effectiveness of the estimation approach proposed in this paper.     

Constrained predictive synchronization of discrete-time chaotic Lur’e systems with time-varying delayed feedback control

This paper presents a predictive synchronization method for discrete-time chaotic Lur’e systems with input constraints by using time-varying delayed feedback control. Based on the model predictive control scheme, a delay-dependent stabilization criterion is derived for the synchronization of chaotic systems that is represented by Lur’e systems with input constraints. By constructing a suitable Lyapunov–Krasovskii functional and combining with a reciprocally convex combination technique, a delay-dependent stabilization condition for synchronization is obtained via linear matrix inequality (LMI) formulation. The control inputs are obtained by solving a min-max problem subject to cost monotonicity, which is expressed in terms of LMIs. The effectiveness of the proposed method will be verified throughout a numerical example.     

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 augmented Lyapunov–Krasovskii functional approach to stability analysis of neural networks with time-varying delays

This paper is concerned with the problem of stability analysis for neural networks with time-varying delays. By constructing a newly augmented Lyapunov functional and some novel techniques, delay-dependent criteria to guarantee the asymptotic stability of the concerned networks are derived in terms of linear matrix inequalities (LMIs). The improvement of feasible region of the proposed criteria comparing with the previous works is shown by two numerical examples.     

Projective synchronization of neural networks with mixed time-varying delays and parameter mismatch

In this paper, the projective synchronization of neural networks with mixed time-varying delays and parameter mismatch is discussed. Due to parameter mismatch and projective factor, complete projective synchronization cannot be achieved. Therefore, a new weak projective synchronization scheme is proposed to ensure that coupled neural networks are in a state of synchronization with an error level. Several criteria are derived and the error level is estimated by applying a generalized Halanay inequality and matrix measure. Finally, a numerical example is given to verify the efficiencies of theoretical results.     

Output feedback ℋ∞ synchronization for delayed chaotic neural networks

In this paper, we propose a new output feedback ?_∞ synchronization method for delayed chaotic neural networks with external disturbance. Based on Lyapunov–Krasovskii theory and linear matrix inequality (LMI) approach, the output feedback ?_∞ synchronization controller is presented to not only guarantee stable synchronization, but also reduce the effect of external disturbance to an ?_∞ norm constraint. The proposed controller can be obtained by solving the LMI problem. An illustrative example is given to demonstrate the effectiveness of the proposed method.     

Global stability in switched recurrent neural networks with time-varying delay via nonlinear measure

In this paper, based on switched systems and recurrent neural networks (RNNs) with time-varying delay, the model of switched RNNs is formulated. Global asymptotical stability (GAS) and global robust stability (GRS) for such switched neural networks are studied by employing nonlinear measure and linear matrix inequality (LMI) techniques. Some new sufficient conditions are obtained to ensure GAS or GRS of the unique equilibrium of the proposed switched system. Furthermore, the proposed LMI results are computationally efficient as it can be solved numerically with standard commercial software. Finally, three examples are provided to illustrate the usefulness of the results.