Wenbing Zhang

Neural networks letter: Stability of delayed neural networks with time-varying impulses

This paper addresses the stability problem of a class of delayed neural networks with time-varying impulses. One important feature of the time-varying impulses is that both the stabilizing and destabilizing impulses are considered simultaneously. Based on the comparison principle, the stability of delayed neural networks with time-varying impulses is investigated. Finally, the simulation results demonstrate the effectiveness of the results.

Stochastic stability of Markovian jumping genetic regulatory networks with mixed time delays

Abstract In this paper, the stability analysis problem is investigated for a class of Markovian jumping genetic regulatory networks (GRNs) with mixed time delays (discrete time delays and distributed time delays) and stochastic perturbations. The main purpose of the addressed stability analysis problem is to establish some easy-to-verify conditions under which the dynamics of the true concentrations of the messenger ribonucleic acid and protein is asymptotically stable. By utilizing a more general Lyapunov–Krasovskii functional based on the idea of “delay decomposing” and the LMI (linear matrix inequality) technique, we derive sufficient delay-dependent conditions ensuring the asymptotically stability of the GRNs with mixed time delays and noise perturbations in terms of LMI. Finally, simulation examples are exploited to illustrate the effectiveness of the developed theoretical results.

New robust stability analysis for genetic regulatory networks with random discrete delays and distributed delays

This paper investigates the delay-probability-distribution-dependent stability problem of stochastic genetic regulatory networks (GRNs) with random discrete time delays and distributed time delays which exist in both translation process and feedback regulation process. The information of the probability distribution of the discrete time delays is considered and transformed into parameter matrices of the GRN models. By introducing a new Lyapunov functional which takes into account the ranges of delays and employing some free-weighting matrices, some new delay-probability-distribution-dependent stability criteria are established in the form of linear matrix inequalities (LMIs) to guarantee the GRNs to be asymptotically stable in the mean square. In addition, when estimating the upper bounds of the derivative of Lyapunov functionals, we carefully handle the additional useful terms about the distributed delays, which may lead to the less conservative results. The new criteria are applicable to both slow and fast time delays. Finally, numerical examples are given to illustrate the effectiveness of our theoretical results and less conservativeness of the proposed method.

Dissipativity analysis of singular systems with Markovian jump parameters and mode-dependent mixed time-delays

In this paper, the problem of delay-dependent @a-dissipativity analysis is investigated for a general class of singular systems with Markovian jump parameters and mode-dependent mixed time-delays. By using the novel Lyapunov-Krasovskii functional and stochastic analysis technology, the new criteria are derived to guarantee that the addressed singular systems are stochastically admissible and strictly (Q,R,S)-@a-dissipative. Numerical examples are presented to illustrate the effectiveness and less conservativeness of the proposed theoretical results.

Stabilizing and synchronizing the Markovian jumping neural networks with mode-dependent mixed delays based on quantized state feedback

Abstract In this paper, stabilization and synchronization control problems are considered for Markovian jumping neural networks with mode-dependent mixed time delays subject to quantization and packet dropout. By using the novel Lyapunov–Krasovskii functional, stochastic analysis technology and quantization feedback method, the stabilization problem is solved for the addressed neural networks firstly. Also, it is assumed that system state is quantized before being communicated. Then the sufficient condition for the existence of an admissible controller is established to ensure the asymptotic synchronization of the resulting closed-loop coupled neural networks. Finally, two numerical examples are presented to show the validity of our theoretical analysis results.

Synchronization of Markovian jump genetic oscillators with nonidentical feedback delay

This paper concerns the exponential synchronization problem of Markovian jump genetic oscillators with partly unknown transition probabilities. We consider three types of feedback delays: feedback with nonidentical delay, feedback without self delay and feedback with identical delay. Based on Lyapunov functional methods and stochastic analysis techniques, the synchronization problem of genetic oscillators are derived. Finally, an example is given to illustrate the effectiveness of the derived results.

Robust stability of interval genetic regulatory networks with multiple time-varying delays

In this paper, the delay-dependent stability analysis problem for a class of genetic regulatory networks(GRNs) with multiple time-varying delays and interval parameter uncertainties is studied. By employing a new Lyapunov-Krasovskii functional, some delay-dependent stability criteria of interval GRNs are derived in the form of linear matrix inequali-ties(LMIs) which can be easily checked by Matlab Toolbox. Finally, a numerical examples are used to demonstrate the usefulness of the main results and effectiveness of the derived conditions.