Exponential Stabilization of Memristor-based Chaotic Neural Networks with Time-Varying Delays via Intermittent Control

This paper is concerned with the global exponential stabilization of memristor-based chaotic neural networks with both time-varying delays and general activation functions. Here, we adopt nonsmooth analysis and control theory to handle memristor-based chaotic neural networks with discontinuous right-hand side. In particular, several new sufficient conditions ensuring exponential stabilization of memristor-based chaotic neural networks are obtained via periodically intermittent control. In addition, the proposed results here are easy to verify and they also extend the earlier publications. Finally, numerical simulations illustrate the effectiveness of the obtained results.

Mode-dependent stochastic stability criteria of fuzzy Markovian jumping neural networks with mixed delays

This paper investigates the stochastic stability of fuzzy Markovian jumping neural networks with mixed delays in mean square. The mixed delays include time-varying delay and continuously distributed delay. By using the Lyapunov functional method, Jensen integral inequality, the generalized Jensen integral inequality, linear convex combination technique and the free-weight matrix method, several novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the considered networks in mean square. The proposed results, which do not require the differentiability of the activation functions, can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature.

Further improvement on delay-dependent robust stability criteria for neutral-type recurrent neural networks with time-varying delays

This paper is concerned with the problem of improved delay-dependent robust stability criteria for neutral-type recurrent neural networks (NRNNs) with time-varying delays. Combining the Lyapunov-Krasovskii functional with linear matrix inequality (LMI) techniques and integral inequality approach (IIA), delay-dependent robust stability conditions for RNNs with time-varying delay, expressed in terms of quadratic forms of state and LMI, are derived. The proposed methods contain the least number of computed variables while maintaining the effectiveness of the robust stability conditions. Both theoretical and numerical comparisons have been provided to show the effectiveness and efficiency of the present method. Numerical examples are included to show that the proposed method is effective and can provide less conservative results.

Exponential stabilization for sampled-data neural-network-based control systems

This paper investigates the problem of sampled-data stabilization for neural-network-based control systems with an optimal guaranteed cost. Using time-dependent Lyapunov functional approach, some novel conditions are proposed to guarantee the closed-loop systems exponentially stable, which fully use the available information about the actual sampling pattern. Based on the derived conditions, the design methods of the desired sampled-data three-layer fully connected feedforward neural-network-based controller are established to obtain the largest sampling interval and the smallest upper bound of the cost function. A practical example is provided to demonstrate the effectiveness and feasibility of the proposed techniques.

Delay-decomposing approach to robust stability for switched interval networks with state-dependent switching

This paper is concerned with a class of nonlinear uncertain switched networks with discrete time-varying delays . Based on the strictly complete property of the matrices system and the delay-decomposing approach, exploiting a new Lyapunov-Krasovskii functional decomposing the delays in integral terms, the switching rule depending on the state of the network is designed. Moreover, by piecewise delay method, discussing the Lyapunov functional in every different subintervals, some new delay-dependent robust stability criteria are derived in terms of linear matrix inequalities, which lead to much less conservative results than those in the existing references and improve previous results. Finally, an illustrative example is given to demonstrate the validity of the theoretical results.

Improved delay-dependent stability analysis for neural networks with time-varying delays

In this paper, the problem of delay-dependent asymptotic stability analysis for neural networks with time-varying delays is considered. A new class of Lyapunov functional is proposed by considering the information of neuron activation functions adequately. By using the delay-partitioning method and the reciprocally convex technique, some less conservative stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are given to illustrate the effectiveness of the derived method.

Improved conditions for passivity of neural networks with a time-varying delay

The passivity of neural networks with a time-varying delay and norm-bounded parameter uncertainties is investigated in this paper. A complete delay-decomposing approach is employed to construct a Lyapunov-Krasovskii functional. Then, by utilizing a segmentation technique to consider the time-varying delay and its derivative and introducing some free-weighting matrices to express the relationship between the time-varying delay and its varying interval, some improved passivity criteria are derived. Finally, two numerical examples are given to show the effectiveness and the merits of the proposed method.

Delay-dependent stability criteria for reaction–diffusion neural networks with time-varying delays

This paper studies the global asymptotic stability problem of a class of reaction–diffusion neural networks with time-varying delays. To overcome the difficulty caused by the partial differential term, a novel Lyapunov–Krasovskii functional is proposed, and a partial differential equation technique together with a linear operator approach are also applied to obtain the delay-dependent stability criteria, which are less conservative than the existing results. Finally, simulation examples are given to verify and illustrate the theoretical analysis.

Stochastic synchronization of Markovian jump neural networks with time-varying delay using sampled data

In this paper, the problem of sampled-data synchronization for Markovian jump neural networks with time-varying delay and variable samplings is considered. In the framework of the input delay approach and the linear matrix inequality technique, two delay-dependent criteria are derived to ensure the stochastic stability of the error systems, and thus, the master systems stochastically synchronize with the slave systems. The desired mode-independent controller is designed, which depends upon the maximum sampling interval. The effectiveness and potential of the obtained results is verified by two simulation examples.

Finite-time H∞ control for a class of Markovian jump systems with mode-dependent time-varying delays via new Lyapunov functionals

This paper is concerned with the problem of finite-time H∞ control for a class of Markovian jump systems with mode-dependent time-varying delays via new Lyapunov functionals. In order to reduce conservatism, a new Lyapunov-Krasovskii functional is constructed. Based on the derived condition, the reliable H∞ control problem is solved, and the system trajectory stays within a prescribed bound during a specified time interval. Finally, numerical examples are given to demonstrate the proposed approach is more effective than some existing ones.

New algebraic criteria for synchronization stability of chaotic memristive neural networks with time-varying delays

In this brief, we consider the exponential synchronization of chaotic memristive neural networks with time-varying delays using the Lyapunov functional method and inequality technique. The dynamic analysis here employs the theory of differential equations with discontinuous right-hand side as introduced by Filippov. The designing laws in the synchronization of neural networks are proposed via state or output coupling. In addition, the new proposed algebraic criteria are very easy to verify, and they also enrich and improve the earlier publications. Finally, an example is given to show the effectiveness of the obtained results.

Exponential stabilization of delayed recurrent neural networks: A state estimation based approach

This paper is concerned with the stabilization problem of delayed recurrent neural networks. As the states of neurons are usually difficult to be fully measured, a state estimation based approach is presented. First, a sufficient condition is derived such that the augmented system under consideration is globally exponentially stable. Then, by employing a decoupling technique, the gain matrices of the controller and state estimator are achieved by solving some linear matrix inequalities. Finally, a delayed neural network with chaotic behaviors is exploited to demonstrate the applicability of the developed result.

Combined convex technique on delay-dependent stability for delayed neural networks

In this brief, by employing an improved Lyapunov-Krasovskii functional (LKF) and combining the reciprocal convex technique with the convex one, a new sufficient condition is derived to guarantee a class of delayed neural networks (DNNs) to be globally asymptotically stable. Since some previously ignored terms can be considered during the estimation of the derivative of LKF, a less conservative stability criterion is derived in the forms of linear matrix inequalities, whose solvability heavily depends on the information of addressed DNNs. Finally, we demonstrate by two numerical examples that our results reduce the conservatism more efficiently than some currently used methods.