Kaibo Shi

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.

Stochastic mean square exponential synchronisation of time-varying complex dynamical networks via pinning control

ABSTRACT This paper investigates the problem of stochastic mean square exponential synchronisation of complex dynamical networks with time-varying delay via pinning control. By applying the Lyapunov method and stochastic analysis, criteria on mean square exponential synchronisation are established under linear feedback pinning control and adaptive feedback pinning control, which depend on the time-varying delay and stochastic perturbation. These results complement and improve the previously known results. Two numerical examples are given to illustrate the effectiveness and correctness of the derived theoretical results.

Nonfragile H∞ control for periodic stochastic systems with probabilistic measurement

This paper addresses the problem of nonfragile H∞ control for periodic stochastic systems with probabilistic measurement. A novel Lyapunov-Krasovskii functional is formulated, which makes full use of both delay and its change rate. In view of the measurement signal, the mode-dependent stochastic variables are employed and new sufficient conditions are achieved. Finally, two numerical examples are worked out to demonstrate the effectiveness of the proposed control design.

Improved results on synchronisation of delayed complex dynamical networks via sampled-data control

ABSTRACT This paper focuses on the synchronisation problem of delayed complex dynamical networks via sampled-data control. A novel input-delay-dependent Lyapunov–Krasovskii functional (LKF) is constructed for the first time, which can make full use of the information on the input delay. To strengthen the combinations of the vectors in the resulting augmented vector, a new zero value equality is founded. Based on the input-delay-dependent LKF and zero value equality, synchronisation criteria are established. In comparison with some existing synchronisation criteria, the criteria in this paper are less conservative. The desired sampled-data controller is designed by solving a set of linear matrix inequalities. Finally, numerical examples are given to demonstrate the superiorities of proposed results.

Exponential stability and extended dissipativity criteria for generalized discrete-time neural networks with additive time-varying delays

This paper is concerned with exponential stability and extended dissipativity criteria for generalized discrete-time neural networks (GDNNs) with additive time-varying delays. The generalized dissipativity analysis combines a few previous results into a framework, such as l2−l∞ performance, H∞ performance, passivity performance, strictly (Q,S,R)−γ−dissipative and strictly (Q,S,R)−dissipative. The definition of exponential stability for GDNNs is given with a new and more appropriate expression. A novel augmented Lyapunov-Krasovskii functional (LKF) which involves more information about the additive time-varying delays is constructed. By introducing more zero equalities and using a new double summation inequality together with Finsler’s lemma, an improved delay-dependent exponential stability and extended dissipativity criterion are derived in terms of convex combination technique (CCT). Finally, numerical examples are given to illustrate the usefulness and advantages of the proposed methods.

Stochastic switched sampled-data control for synchronization of delayed chaotic neural networks with packet dropout

This paper addresses the exponential synchronization issue of delayed chaotic neural networks (DCNNs) with control packet dropout. A novel stochastic switched sampled-data controller with time-varying sampling is developed in the frame of the zero-input strategy. First, by making full use of the available characteristics on the actual sampling pattern, a newly loop-delay-product-type Lyapunov–Krasovskii functional (LDPTLKF) is constructed via introducing a matrix-refined-function, which can reflect the information of delay variation. Second, based on the LDPTLKF and the relaxed Wirtinger-based integral inequality (RWBII), novel synchronization criteria are established to guarantee that DCNNs are synchronous exponentially when the control packet dropout occurs in a random way, which obeys certain Bernoulli distributed white noise sequences. Third, a desired sampled-data controller can be designed on account of the proposed optimization algorithm. Finally, the effectiveness and advantages of the obtained results are illustrated by two numerical examples with simulations.

Extended robust global exponential stability for uncertain switched memristor-based neural networks with time-varying delays

Abstract This paper is concerned with the problem of global exponential stability for uncertain memristive-based neural networks (UMNNs) with time-varying delays and switching parameters subject to unstable subsystems. Different from most of the existing papers, the considered uncertain switched MNNs with discrete-delays are modeled as switched neural networks (SNNs) with uncertain time-varying parameters. Based on multiple Lyapunov–Krasovskii functional (MLF) approach, average dwell time (ADT) technique and mode-dependent average dwell time (MDADT) method, some LMIs-based stability criteria are derived to design the switching signal and guarantee the exponential stability of the considered uncertain switched neural networks. By exploring the mode-dependent property of each subsystem, all the subsystems are categorized into stable and unstable ones. The concerned SNNs with both stable and unstable subsystems are more general and applicable than the existing models of SNNs only view all subsystems being stable, thus getting less conservatism criteria. The proposed sufficient conditions can be simplified into the forms of LMIs for conveniently using Matlab LMI toolbox. Finally, two numerical examples are exploited to demonstrate the effectiveness and applicability of the proposed theoretical 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.