Ruimei Zhang

Event-triggered sampling control for stability and stabilization of memristive neural networks with communication delays

This paper investigates the global asymptotic stability and stabilization of memristive neural networks (MNNs) with communication delays via event-triggered sampling control. First, based on the novel approach in Lemma 1, the concerned MNNs are converted into traditional neural networks with uncertain parameters. Next, a discrete event-triggered sampling control scheme, which only needs supervision of the system state at discrete instants, is designed for MNNs for the first time. Thanks to this controller, the number of control updates could greatly reduce. Then, by getting utmost out of the usable information on the actual sampling pattern, a newly augmented Lyapunov-Krasovskii functional (LKF) is constructed to formulate stability and stabilization criteria. It should be mentioned that the LKF is positive definite only at endpoints of each subinterval of the holding intervals but not necessarily positive definite inside the holding intervals. Finally, the feasibility and effectiveness of the proposed results are tested by two numerical examples.

Novel master–slave synchronization criteria of chaotic Lur’e systems with time delays using sampled-data control

Abstract This paper investigates the problem of master–slave synchronization of chaotic Lur’e systems (CLSs) with time delays by sampled-data control. First, a novel Lyapunov–Krasovskii functional (LKF) is constructed with some new augmented terms, which can fully capture the system characteristics and the available information on the actual sampling pattern. In comparison with existing results, the constraint condition of the positive definition of the LKF is more relax, since it is positive definite only requiring at sampling instants. Second, based on the LKF, a less conservative synchronization criterion is established. Third, the desired estimator gain can be designed in terms of the solution to linear matrix inequalities (LMIs). The obtained conditions ensure the master–slave synchronization of CLSs under a longer sampling period than remarkable existing works. Finally, three numerical simulations of Chua’s circuit and neural network are provided to show the effectiveness and advantages of the proposed results.

Sampled-data synchronization of chaotic Lur’e systems via input-delay-dependent-free-matrix zero equality approach

Abstract This paper focuses on the sampled-data synchronization problem of chaotic Lur’e systems (CLSs) by using sampled output of the systems with variable sampling rates. One novel approach, input-delay-dependent-free-matrix zero equality (IDDFMZE) approach, is proposed for the first time. The IDDFMZE approach can not only fully capture the available information on the actual sampling pattern, but deploy more system information at the dynamic partitioning point. A new Lyapunov–Krasovskii functional (LKF) with some new terms is constructed, which can use more information of the activation function at the dynamic partitioning point. Based on the presented IDDFMZE approach and the constructed LKF, developed synchronization criterion is obtained in the form of linear matrix inequalities (LMIs). The desired sampled-data controller is designed under larger sampling period. Finally, the superiority of proposed results is shown by two numerical examples.

Sampled-data synchronization control for Markovian delayed complex dynamical networks via a novel convex optimization method

Abstract This paper investigates the problem of exponential synchronization for Markovian delayed complex dynamical networks (CDNs) via a sampled-data control scheme. First, a modified piecewise augmented Lyapunov–Krasovskii functional (LKF) is constructed, which can fully capture the system characteristics and the available information on the actual sampling pattern. In comparison with existing results, the constraint condition of the positive definition of the LKF is more relax, since we take the LKF as a whole to examine its positive definite instead of restricting each term of it to positive definite. Second, by developing a novel convex optimization method, improved criteria are derived. Third, based on a new inequality of the neuron activation function, the desired sampled-data controller is designed under a larger sampling interval. Finally, three numerical examples are provided to show the effectiveness and advantages of the proposed results.

Nonfragile Sampled-Data Synchronization for Delayed Complex Dynamical Networks With Randomly Occurring Controller Gain Fluctuations

In this paper, the problem of nonfragile sampled-data synchronization of delayed complex dynamical networks with randomly occurring controller gain fluctuations (ROCGFs) is studied. First, more applicable nonfragile memory sampled-data controllers are designed, which involve the signal transmission delay and ROCGFs. The controller gain fluctuations appear in a random way, which obey certain Bernoulli distributed white noise sequences. Second, a modified piecewise Lyapunov–Krasovskii functional (LKF), which involves cubic sawtooth structure term, is constructed for the first time. Third, based on the LKF, less conservative synchronization criteria are established. In comparison with the existing results, the constraint condition of the positive definition of the LKF is less restrictive, since it does not need to be positive definite for all time, but is only required to be positive definite at sampling times. Finally, the effectiveness and advantages of the obtained results are illustrated by two numerical examples.

Improved results on sampled-data synchronization of Markovian coupled neural networks with mode delays

Abstract This paper studies the problem of synchronization for Markovian coupled neural networks (CNNs) with mode delays via sampled-data control. First, a new augmented time-dependent Lyapunov–Krasovskii functional (LKF) is constructed, which can fully capture the information of the sawtooth structure. Second, in order to strengthen the combinations of some resulting vectors, a new zero value equality is founded. Third, based on the augmented time-dependent LKF and zero value equality, synchronization criteria are derived. The desired mode-dependent sampled-data controllers can be obtained by solving a set of linear matrix inequalities (LMIs). In comparison with some existing results, our results are not only less conservative but also with reduced calculation complexity. Finally, two numerical examples are provided to show the effectiveness and advantages of the proposed results.

Novel discontinuous control for exponential synchronization of memristive recurrent neural networks with heterogeneous time-varying delays

Abstract This paper investigates the exponential synchronization problem of memristive recurrent neural networks (MRNNs) with heterogeneous time-varying delays (HTVDs). First, a novel discontinuous feedback control is designed, in which a tunable scalar is introduced. The tunable scalar makes the controller more flexible in reducing the upper bound of the control gain. Based on this control scheme, the double integral term can be successfully used to construct the LKF. Second, New method for tackling memristive synaptic weights and new estimation technique are presented. Third, based on the LKF and estimation technique, synchronization criterion is derived. In comparison with existing results, the established criterion is less conservatism thanks to the double integral term of the LKF. Finally, numerical simulations are presented to validate the effectiveness and advantages of the proposed results.

A new method for exponential synchronization of memristive recurrent neural networks

Abstract This paper investigates the exponential synchronization problem of memristive recurrent neural networks (MRNNs). A novel approach, switching matrix approach, is considered to study synchronization of MRNNs for the first time. All the matrices in the constructed Lyapunov–Krasovskii functional (LKF) are switching according to different switching rules. Based on the switching matrix approach, a new synchronization criterion is established in the form of linear matrix inequalities (LMIs). Compared with some existing methods, the switching matrix approach is more flexible and can improve the synchronization performance with low control cost. Finally, numerical simulations are provided to show the effectiveness and advantages of the proposed results.

Novel Lebesgue-integral-based approach to improved results for neural networks with additive time-varying delay components

Abstract In this paper, we propose a novel Lebesgue-integral-based approach to investigate the stability for neural networks with additive time-varying delay components. Based on the Lebesgue integral theory, a new Lyapunov–Krasovskii functional (LKF), which involves Lebesgue integral terms, is constructed, and the corresponding stability theorem is derived. More information on the neuron activation functions and fewer matrix variables are involved in the constructed LKF. Then, on the basis of the above method, an improved stability criterion is developed. Compared with the existing results, the derived stability condition is with less conservatism and computational burden. Moreover, the obtained criterion is extended to study the system with a single time-varying delay. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.