Qiankun Song

Passivity analysis of discrete-time stochastic neural networks with time-varying delays

In this paper, the problem of passivity analysis is investigated for a class of discrete-time stochastic neural networks with time-varying delays. For the neural networks under study, a generalized activation function is considered, where the traditional assumptions on the boundedness, monotony and differentiability of the activation functions are removed. By constructing proper Lyapunov-Krasovskii functional and employing a combination of the free-weighting matrix method and stochastic analysis technique, a delay-dependent passivity condition is derived in terms of linear matrix inequalities (LMIs). Furthermore, when the parameter uncertainties appear in the discrete-time stochastic neural networks with time-varying delays, a delay-dependent robust passivity condition is also presented. An example is given to show the effectiveness of the proposed criterion.

Exponential stability of recurrent neural networks with both time-varying delays and general activation functions via LMI approach

In this paper, the problem on exponential stability analysis of recurrent neural networks with both time-varying delays and general activation functions is considered. Neither the boundedness and the monotony on these activation functions nor the differentiability on the time-varying delays are assumed. By employing Lyapunov functional and the free-weighting matrix method, several sufficient conditions in linear matrix inequality form are obtained to ensure the existence, uniqueness and global exponential stability of equilibrium point for the neural networks. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The proposed stability results are less conservative than some recently known ones in the literature, which is demonstrated via an example with simulation.

Global stability of complex-valued neural networks with both leakage time delay and discrete time delay on time scales

In this paper, the complex-valued neural networks with both leakage time delay and discrete time delay as well as two types of activation functions on time scales are considered. By using the fixed point theory, a criterion for checking the existence, uniqueness of the equilibrium point for the considered complex-valued neural networks is presented. By constructing appropriate Lyapunov-Krasovskii functionals, and employing the free weighting matrix method, several delay-dependent criteria for checking the global stability of the addressed complex-valued neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Three examples with simulations are given to show the effectiveness and less conservatism of the proposed criteria.

Dynamical behaviors of discrete-time fuzzy cellular neural networks with variable delays and impulses

Abstract In this paper, the discrete-time fuzzy cellular neural network with variable delays and impulses is considered. Based on M -matrix theory and analytic methods, several simple sufficient conditions checking the global exponential stability and the existence of periodic solutions are obtained for the neural networks. Moreover, the estimation for exponential convergence rate index is proposed. The obtained results show that the stability and periodic solutions still remain under certain impulsive perturbations for the neural network with stable equilibrium point and periodic solutions. Some examples with simulations are given to show the effectiveness of the obtained results.

Global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects

In this paper, the global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects is discussed. By employing Lyapunov functional method and using matrix inequality technique, several sufficient conditions in complex-valued linear matrix inequality form are obtained to ensure the existence, uniqueness and global exponential stability of equilibrium point for the considered neural networks. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The proposed stability results are less conservative than some recently known ones in the literatures, which is demonstrated via two examples with simulations.

Stability analysis of complex-valued neural networks with probabilistic time-varying delays

In this paper, the stability of complex-valued neural networks with probabilistic time-varying delays is investigated. Two important integral inequalities that include Jensen?s inequality as a special case are developed. By constructing proper Lyapunov-Krasovskii functional and employing inequality technique, several delay-distribution-dependent sufficient conditions are obtained to guarantee the global asymptotic and exponential stability of the addressed neural networks. These conditions are expressed in terms of complex-valued LMIs, which can be checked numerically using the effective YALMIP toolbox in MATLAB. An example with simulations is given to show the effectiveness of the obtained results.

Finite-time stability analysis of fractional-order neural networks with delay

Stability analysis of fractional-order neural networks with delay is addressed in this paper. By using the contracting mapping principle, method of iteration and inequality techniques, a sufficient condition is established to ensure the existence, uniqueness and finite-time stability of the equilibrium point of the proposed networks. Finally, based on the Predictor-Corrector Approach, two numerical examples are presented to illustrate the validity and feasibility of the obtained result.

Stability criterion of complex-valued neural networks with both leakage delay and time-varying delays on time scales

In this paper, the problem on the global exponential stability of complex-valued neural networks with both leakage delay and time-varying delays on time scales is discussed. By constructing appropriate Lyapunov-Krasovskii functionals and using matrix inequality technique, a delay-dependent condition to assure the global exponential stability for the considered neural networks is established. The condition is expressed in complex-valued linear matrix inequality, which can be checked numerically using the effective YALMIP toolbox in MATLAB. An example with simulations is given to show the effectiveness of the obtained result.

Design of controller on synchronization of chaotic neural networks with mixed time-varying delays

In this paper, the problem on synchronization is investigated for neural networks with discrete and distributed time-varying delays as well as generalized activation functions. By constructing proper Lyapunov-Krasovskii functional and employing a combination of the free-weighting matrix method, Newton-Leibniz formulation and inequality technique, the controllers are, respectively, designed to achieve the asymptotical and exponential synchronization of the addressed neural networks. The provided conditions are expressed in terms of LMIs, and are dependent on both the discrete and distributed time delays. A simulation example is given to show the effectiveness and less conservatism of the obtained conditions. It is noteworthy that the traditional assumptions on the differentiability of the time-varying delays and the boundedness of its derivative are removed.

Synchronization analysis of coupled connected neural networks with mixed time delays

In this paper, the global exponential synchronization of coupled connected neural networks with both discrete and distributed delays is investigated under mild condition, assuming neither the differentiability and strict monotonicity for the activation functions nor the diagonal for the inner coupling matrices. By employing a new Lyapunov-Krasovskii functional, applying the theory of Kronecker product of matrices and the linear matrix inequality (LMI) technique, several delay-dependent sufficient conditions in LMI form are obtained for global exponential synchronization of such systems. Moreover, the decay rate is estimated. The proposed LMI approach has the advantage of considering the difference of neuronal excitatory and inhibitory efforts, which is also computationally efficient as it can be solved numerically using efficient Matlab LMI toolbox, and no tuning of parameters is required. In addition, the proposed results generalize and improve the earlier publications. An example with simulation is given to show the effectiveness of the obtained results.