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.     

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.     

Global synchronization of stochastic delayed complex networks

This paper is concerned with the delay-dependent synchronization criterion for stochastic complex networks with time delays. Firstly, expectations of stochastic cross terms containing the It? integral are investigated by utilizing stochastic analysis techniques. In fact, in order to obtain less conservative delay-dependent conditions for stochastic delay systems including stochastic complex (or neural) networks with time delays, how to deal with expectations of these stochastic cross terms is an important problem, and expectations of these stochastic terms were not dealt with properly in many existing results. Then, based on the investigation of expectations of stochastic cross terms, this paper proposes a novel delay-dependent synchronization criterion for stochastic delayed complex networks. In the derivation process, the mathematical development avoids bounding stochastic cross terms. Thus, the method leads to a simple criterion and shows less conservatism. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.     

Switched exponential state estimation of neural networks based on passivity theory

In this paper, a new exponential state estimation method is proposed for switched Hopfield neural networks based on passivity theory. Through available output measurements, the main purpose is to estimate the neuron states such that the estimation error system is exponentially stable and passive from the control input to the output error. Based on augmented Lyapunov–Krasovskii functional, Jensen’s inequality, and linear matrix inequality (LMI), a new delay-dependent state estimator for switched Hopfield neural networks can be achieved by solving LMIs, which can be easily facilitated by using some standard numerical packages. The unknown gain matrix is determined by solving delay-dependent LMIs. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.     

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.     

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.     

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.     

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.     

Passivity analysis of uncertain neural networks with mixed time-varying delays

This paper addresses the passivity problem for uncertain neural networks with both discrete and distributed time-varying delays. It is assumed that the parameter uncertainties are norm-bounded. By construction of an augmented Lyapunov–Krasovskii functional and utilization of zero equalities, improved passivity criteria for the networks are derived in terms of linear matrix inequalities (LMIs) via new approaches. Through three numerical examples, the effectiveness to enhance the feasible region of the proposed criteria is demonstrated.     

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.     

Global asymptotic stability of cellular neural networks with proportional delays

Proportional delay, which is different from distributed delay, is a kind of unbounded delay. The proportional delay system as an important mathematical model often rises in some fields such as physics, biology systems, and control theory. In this paper, the uniqueness and the global asymptotic stability of equilibrium point of cellular neural networks with proportional delays are analyzed. By using matrix theory and constructing suitable Lyapunov functional, delay-dependent and delay-independent sufficient conditions are obtained for the global asymptotic stability of cellular neural networks with proportional delays. These results extend previous works on these issues for the delayed cellular neural networks. Two numerical examples and their simulation are given to illustrate the effectiveness of obtained results.     

Globally exponential stability of stochastic neutral-type delayed neural networks with impulsive perturbations and Markovian switching

The problem of globally exponential stability of stochastic neutral-type delayed neural networks with impulsive perturbations and Markovian switching is studied in this paper. By using the Lyapunov?CKrasovskii method and the stochastic analysis approach, a sufficient condition to ensure globally exponential stability for the stochastic neutral-type delayed neural networks with impulsive perturbations and Markovian switching is derived. Finally, a numerical example is given to illustrate the effectiveness of the result proposed in this paper.     

Passivity analysis of delayed neural networks with discontinuous activations via differential inclusions

Without assuming the boundedness and monotonicity of neuron activations, we investigate passivity of delayed neural networks with discontinuous activations. Based on differential inclusion theory, sufficient conditions are established in form of linear matrix inequality by employing the generalized Lyapunov approach. In addition, a kind of control input is designed to stabilize neural network with activation functions having special form. Finally, some numerical examples are proposed to show the effectiveness of developed results.     

Dynamic stability recognition of cylindrical shallow shells in Kelvin–Voigt viscoelastic medium under transverse white noise excitation

Nonlinear Dynamics - This paper investigates the problem of delay-dependent dissipativity for a class of Markovian jump neural networks with a time-varying delay. A generalized integral inequality...     

Delay-dependent robust stability and H_∞ analysis of stochastic systems with time-varying delay

This paper investigates the robust stochastic stability and H∞ analysis for stochastic systems with time-varying delay and Markovian jump. By using the freeweighting matrix technique, i.e., He's technique, and a stochastic Lyapunov-Krasovskii functional, new delay-dependent criteria in terms of linear matrix inequalities are derived for the the robust stochastic stability and the H∞ disturbance attenuation. Three numerical examples are given. The results show that the proposed method is efficient and much less conservative than the existing results in the literature.     

Exponential stability in the mean square for stochastic neural networks with mixed time-delays and Markovian jumping parameters

In this paper, the stability analysis problem is considered for a class of stochastic neural networks with mixed time-delays and Markovian jumping parameters. The mixed delays include discrete and distributed time-delays, and the jumping parameters are generated from a continuous-time discrete-state homogeneous Markov process. The aim of this paper is to establish some criteria under which the delayed stochastic neural networks are exponentially stable in the mean square. By constructing suitable Lyapunov functionals, several stability conditions are derived on the basis of inequality techniques and the stochastic analysis. An example is also provided in the end of this paper to demonstrate the usefulness of the proposed criteria.     

Improved delay-dependent stability conditions for recurrent neural networks with multiple time-varying delays

This paper investigates the global asymptotic stability problem for recurrent neural networks with multiple time-varying delays. Using the free-weighting matrix technique, and incorporating the interconnected information between the upper bounds of multiple time-varying delays, two less conservative delay-dependent asymptotic stability conditions are proposed, which are expressed by linear matrix inequalities, and can be conveniently solved by the existing softwares. Numerical examples show the reduce conservatism of the obtained conditions.     

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.     

Neurodynamics analysis of brain information transmission

This paper proposes a model of neural networks consisting of populations of perceptive neurons, inter-neurons, and motor neurons according to the theory of stochastic phase resetting dynamics. According to this model, the dynamical characteristics of neural networks are studied in three coupling cases, namely, series and parallel coupling, series coupling, and unilateral coupling. The results show that the indentified structure of neural networks enables the basic characteristics of neural information processing to be described in terms of the actions of both the optional motor and the reflected motor. The excitation of local neural networks is caused by the action of the optional motor. In particular, the excitation of the neural population caused by the action of the optional motor in the motor cortex is larger than that caused by the action of the reflected motor. This phenomenon indicates that there are more neurons participating in the neural information processing and the excited synchronization motion under the action of the optional motor.     

Adaptive synchronization of stochastic neural networks with mixed time delays and reaction–diffusion terms

In this paper, the problem of exponential synchronization is investigated for a class of stochastic perturbed chaotic neural networks with both mixed time delays and reaction?Cdiffusion terms. By employing Lyapunov?CKrasovskii functional and stochastic analysis approaches, an adaptive controller is designed to guarantee the exponential synchronization of proposed neural networks in the mean square. In particular, the mixed time delays in this paper synchronously consist of constant delay in the leakage term (i.e., ??leakage delay??), discrete time-varying delay and distributed time-varying delay which are more general than those discussed in the previous literature. Furthermore, our synchronization criteria are easily verified and do not need to solve any linear matrix inequality. Therefore, the results obtained in this paper generalize and improve those given in the previous literature. Finally, the extensive simulations are performed to show the effectiveness and feasibility of the obtained method.