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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]

Abstract The periodicity problem of a class of Cohen–Grossberg-type fuzzy neural networks with impulses and time-varying delays is concerned in this paper. Via constructing a delay differential inequality, and applying fuzzy theory and the Lyapunov method, several criteria which ensure the existence and exponential stability of the periodic solutions for the considered systems are derived. An example is shown to illustrate the validity of the obtained results. [ABSTRACT FROM AUTHOR]

Abstract This article mainly concerns the synchronization in finite-time to the time-varying delay fractional order memristive competitive neural networks (TMFCNNs) with leakage delay. By means of Fillipov’s theory, Gronwall–Bellman integral inequality, H o ¨ lder’s inequality, and the Caputo derivative properties, the novel algebraic sufficient conditions are proposed to guarantee the synchronization in finite time of addressing TMFCNNs with non-integer order: 0 < p < 1 2 and 1 2 ≤ p < 1 via finite-time output feedback controller. Up to now, there are no relevant results in fractional order competitive-type neural networks, and this article makes filling up for this gap. The obtained results are improved to some existing results on integer-order memristive competitive neural networks. Finally, two numerical examples with simulations are also designed to confirm the merits of the proposed theoretical results, while we estimate the upper bound of the settling time for the synchronization errors. [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, global asymptotic stability of impulsive fractional-order complex-valued neural networks with time delay is considered. By employing contraction mapping principle, comparison theorem and inequality scaling skills, several sufficient conditions to ensure the existence, uniqueness and global asymptotic stability of the equilibrium point for the considered neural networks are established. A numerical example illustrates the validity and feasibility of the obtained result. [ABSTRACT FROM AUTHOR]

This paper is concerned with the passivity problem for neural networks with leakage delay and time-varying transmission delay. Using some novel Lyapunov-Krasovskii (L-K) functionals, and combining with the Wirtinger integral inequality, some less conservative delay-dependent passivity conditions are proposed in terms of linear matrix inequalities (LMIs). Different from the existing approaches, the model transformation is abandoned in this paper, and the proposed L-K functionals incorporate the interconnected terms related to both the leakage delay and the time-varying delay. Numerical examples show that the obtained conditions are less conservative. [ABSTRACT FROM AUTHOR]

In this paper, the non-fragile state estimation problem is investigated for a class of continuous neural networks with time-delays and nonlinear perturbations. The estimator to be designed is of a simple linear structure without requiring the exact information of the activation functions or the time-delays, and is therefore easy to be implemented. Furthermore, the designed estimator gains are allowed to undergo multiplicative parameter variations within a given range and the non-fragility is guaranteed against possible implementation errors. The main purpose of the addressed problem is to design a non-fragile state estimator for the recurrent delayed neural networks such that the dynamics of the estimation error converges to the equilibrium asymptotically irrespective of the admissible parameter variations with the estimator gains. By employing a combination of the Lyapunov functionals and the matrix analysis techniques, sufficient conditions are established to ensure the existence of the desired estimators and the explicit characterization of such estimators are then given via solving a linear matrix inequality. Finally, a simulation example is used to illustrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of designing a non-fragile state estimator for a class of uncertain discrete-time neural networks with time-delays. The norm-bounded parameter uncertainties enter into all the system matrices, and the network output is of a general type that contains both linear and nonlinear parts. The additive variation of the estimator gain is taken into account that reflects the possible implementation error of the neuron state estimator. The aim of the addressed problem is to design a state estimator such that the estimation performance is non-fragile against the gain variations and also robust against the parameter uncertainties. Sufficient conditions are presented to guarantee the existence of the desired non-fragile state estimators by using the Lyapunov stability theory and the explicit expression of the desired estimators is given in terms of the solution to a linear matrix inequality. Finally, a numerical example is given to demonstrate the effectiveness of the proposed design approach. [ABSTRACT FROM AUTHOR]

In this paper, the non-fragile state estimation problem is investigated for a class of discrete-time neural networks subject to Markovian jumping parameters and time delays. In terms of a Markov chain, the mode switching phenomenon at different times is considered in both the parameters and the discrete delays of the neural networks. To account for the possible gain variations occurring in the implementation, the gain of the estimator is assumed to be perturbed by multiplicative norm-bounded uncertainties. We aim to design a non-fragile state estimator such that, in the presence of all admissible gain variations, the estimation error converges to zero exponentially. By adopting the Lyapunov–Krasovskii functional and the stochastic analysis theory, sufficient conditions are established to ensure the existence of the desired state estimator that guarantees the stability of the overall estimation error dynamics. The explicit expression of such estimators is parameterized by solving a convex optimization problem via the semi-definite programming method. A numerical simulation example is provided to verify the usefulness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper investigates the almost sure H ∞ sliding mode control (SMC) problem for nonlinear stochastic systems with Markovian switching and time-delays. An integral sliding surface is first constructed for the addressed system. Then, by employing the stopping time method combined with martingale inequalities, sufficient conditions are established to ensure the almost surely exponential stability and the H ∞ performance of the system dynamics in the specified sliding surface. A SMC law is designed to guarantee the reachability of the specified sliding surface almost surely. Furthermore, the obtained results are applied to a class of special nonlinear stochastic systems with Markovian switching and time-delays, where the desired SMC law is obtained in terms of the solutions to a set of matrix inequalities. Finally, a numerical example is given to show the effectiveness of the proposed SMC scheme. [ABSTRACT FROM AUTHOR]

By using exponential dichotomy theory, contraction mapping principle and discrete-continuous analysis method, we obtain some new sufficient conditions ensuring the existence and global exponential stability of the almost periodic solutions for a class of neutral-type neural networks with distributed leakage delays on time scales. An example is provided to demonstrate the usefulness of the main results obtained. [ABSTRACT FROM AUTHOR]