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Abstract This paper focus on the synchronization of complex-valued neural networks (CVNNs) with both discrete and distributed two additive time-varying delays. By applying matrix inequality technique and exploiting reciprocally convex approach, several delay-dependent criteria are presented in the form of linear matrix inequalities (LMIs) to ensure the global synchronization of CVNNs via structuring an appropriate Lyapunov–Krasovskii functional. An example with simulations is provided to ensure the feasibility of the obtained result. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The stability of fractional-order complex-valued neural networks (FOCVNNs) with probabilistic time-varying delays is investigated in this paper. By constructing suitable Lyapunov–Krasovskii functional and utilizing inequality technique, a complex-valued linear matrix inequality (LMI) criterion guaranteeing the global asymptotic stability of the proposed FOCVNNs is deduced. A numerical example with simulations is provided to demonstrate the feasibility and availability of the obtained theoretical result. [ABSTRACT FROM AUTHOR]

This paper investigates the global asymptotical synchronization of two nonidentical complex-valued neural networks (CVNNs) with leakage delay and time-varying delays via integral sliding mode control approach. A suitable sliding surface and an appropriate Lyapunov–Krasovskii functional are constructed. By using free-weighting matrix method combined with inequality technique, a sliding mode controller is designed to ensure the synchronization for the considered CVNNs. The obtained criterion is presented in the form of complex-valued linear matrix inequalities (LMIs), which could be calculated through YALMIP with solver of SDPT3 in MATLAB. An example is provided to demonstrate the obtained theoretical result. [ABSTRACT FROM AUTHOR]

This paper aims at the problem on state estimation of complex-valued neural networks with two additive time-varying delays. Via selecting appropriate Lyapunov–Krasovskii functionals and utilizing reciprocally convex approach and applying matrix inequality technique to analysis, a delay-dependent sufficient condition is derived in the form of linear matrix inequalities (LMIs) to estimate the neuron state with some observed output measurements so as to guarantee the global asymptotic stability of the error-state system. A numerical example is provided to illustrate the feasibility of the obtained result. [ABSTRACT FROM AUTHOR]

In this paper, the problem on synchronization is investigated for a class of impulsive complex-valued neural networks with discrete and distributed time-varying delays as well as leakage delay. By constructing appropriate Lyapunov–Krasovskii functional, and using Newton–Leibniz formulation, inequality technique and free-weighting matrix method, several sufficient criteria to guarantee the global μ -synchronization are derived for the considered impulsive complex-valued neural networks. The provided conditions are expressed in terms of linear matrix inequalities, and are dependent on the sizes of discrete delays, distributed delays and leakage delay. An example with simulations is provided to verify the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, the boundedness and robust stability for a class of delayed complex-valued neural networks with interval parameter uncertainties are investigated. By using Homomorphic mapping theorem, Lyapunov method and inequality techniques, sufficient condition to guarantee the boundedness of networks and the existence, uniqueness and global robust stability of equilibrium point is derived for the considered uncertain neural networks. The obtained robust stability criterion is expressed in complex-valued LMI, which can be calculated numerically using YALMIP with solver of SDPT3 in MATLAB. An example with simulations is supplied to show the applicability and advantages of the acquired result. [ABSTRACT FROM AUTHOR]

In this paper, the dynamics including boundedness and stability for a general class of complex-valued neural networks with variable coefficients and proportional delays are investigated. By employing inequality techniques and mathematical analysis method, some sufficient criteria to guarantee boundedness and global exponential stability are established for the considered neural networks. As a special case that the coefficients of networks are constants, sufficient criteria are also derived to guarantee the existence, uniqueness and global exponential stability of the equilibrium point. This work generalizes and improves previously known results, and the obtained criteria can be tested and applied easily in practice. An illustrative example demonstrates the feasibility of the proposed results. [ABSTRACT FROM AUTHOR]

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 Lyapunov–Krasovskii 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]