Zhenjiang Zhao

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.

Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays.

This paper investigates the stability problem for a class of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays. By employing the idea of vector Lyapunov function, M-matrix theory and inequality technique, several sufficient conditions are obtained to ensure the global exponential stability of equilibrium point. When the impulsive effects are not considered, several sufficient conditions are also given to guarantee the existence, uniqueness and global exponential stability of equilibrium point. Two examples are given to illustrate the effectiveness and lower level of conservatism of the proposed criteria in comparison with some existing results.

Impulsive effects on stability of discrete-time complex-valued neural networks with both discrete and distributed time-varying delays

In this paper, the impulsive effects on the stability of discrete-time complex-valued neural networks with both discrete and distributed time-varying delays are investigated. Several sufficient conditions are obtained ensuring the existence, uniqueness and global exponential stability of equilibrium point for the considered neural networks by the idea of vector Lyapunov function method, M-matrix theory and analytic technique. Moreover, the estimation for exponential convergence rate index is proposed. An example with simulations is provided to verify the effectiveness of the obtained results.

Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with both leakage and time-varying delays

Finite-time stability of a class of fractional-order complex-valued memristor-based neural networks with both leakage and time-varying delays is investigated in this paper. By employing the set-valued map and differential inclusions, the solutions of memristor-based systems are intended in Filippovs sense. Via using Hlder inequality, GronwallBellman inequality and inequality scaling skills, sufficient conditions to guarantee the stability of the system are derived when 0<<12 and 121, respectively. Finally, two numerical examples are designed to illustrate the validity and feasibility of the obtained results.

Lagrange stability analysis for complex-valued neural networks with leakage delay and mixed time-varying delays

This paper discusses the stability in Lagrange sense for complex-valued neural networks with time-varying discrete delays and distributed delays as well as leakage delay. By constructing an appropriate LyapunovKrasovskii functional, and employing free-weighting-matrix approach and inequality techniques in matrix form, a sufficient criterion to guarantee global exponential stability in Lagrange sense is obtained for the investigated neural networks. The given criterion is delay-dependent and is shown as linear matrix inequalities in complex domain, which can be calculated numerically applying valid YALMIP toolbox in MATLAB. A numerical example is provided to manifest the validity of the proposed result.

Global µ-stability analysis of discrete-time complex-valued neural networks with leakage delay and mixed delays

In this paper, the problem of µ-stability for discrete-time complex-valued neural networks with three kinds of time-delays including leakage delay, discrete delay and distributed delay is considered. Based on contraction mapping theorem and homeomorphism mapping theorem in complex domain, some sufficient conditions are proposed for the existence and uniqueness of the equilibrium point of the addressed neural networks. By constructing an appropriate Lyapunov-Krasovskii functional, and employing the matrix inequality techniques, several delay-dependent criteria for checking the global µ-stability of the complex-valued neural networks are established in linear matrix inequalities (LMIs), which can be checked numerically using the effective YALMIP Tool in MATLAB. As direct applications of these results, we get some criteria on the exponential stability, power-stability and log-stability of the neural networks.

Global stability of quaternion-valued neural networks with non-differentiable time-varying delays

In the paper, the quaternion-valued neural networks (QVNNs) with non-differentiable time-varying delays are considered. Firstly, by using the method of plural decomposition, we decompose the QVNNs into two complex-valued neural networks. Some sufficient criteria in linear matrix inequality (LMI) form are derived to guarantee the existence and uniqueness of the equilibrium point for considered QVNNs by using the homeomorphism mapping principle of complex domain. Secondly, based on applying the free weighting matrix method and constructing appropriate LyapunovKrasovskii functional, several conditions are established in LMIs to ensure the the global stability of QVNNs. Finally, by employing the predictor-corrector approach, two numerical examples are provided to show the feasibility and availability of the obtained result.

Uniform Stability Analysis of Fractional-Order BAM Neural Networks with Delays in the Leakage Terms

A class of fractional-order BAM neural networks with delays in the leakage terms is considered. By using inequality technique and analysis method, several delay-dependent sufficient conditions are established to ensure the uniform stability of such networks. Moreover, the sufficient conditions guaranteeing the existence, uniqueness, and stability of the equilibrium point are also obtained. In addition, three simulation examples are given to demonstrate the effectiveness of the obtained results.