Search

• Demand-driven supply network model with transportation delay is proposed. • State-feedback stabilizing control strategies are designed. • Sufficient conditions that guarantee the stability of the supply network in the form of matrix inequalities are obtained. • The prescribed H∞ disturbance attenuation level under uncertain demand is studied. In this paper, we consider the stabilization strategies for a demand-driven supply network model with transportation delay. Based on Lyapunov stability theory and the robust control approach, we obtain sufficient conditions that guarantee the global asymptotic stability of the supply network in the form of matrix inequalities. Furthermore, state-feedback stabilizing control strategies are designed. We also carry out analysis on the prescribed H ∞ disturbance attenuation level under uncertain demand. Numerical simulation results are presented to verify the effectiveness of the control strategy that is designed. [ABSTRACT FROM AUTHOR]

In this paper, by considering the development of antivirus software always lags behind the emergence of new virus and the point-to-group information propagation mode, a new computer virus model with point to group and discontinuous anti-virus strategy is presented. To the best of our knowledge, this is the first computer virus model that takes into account the effect of discontinuous anti-virus strategy. The dynamic properties of this model are investigated comprehensively. Specifically, it is found that in the case that the equilibrium is asymptotically stable, the convergence to the equilibrium can actually be achieved in finite time, and the time can be estimated in terms of the model parameters, the initial number of the uninfected computer and latent computer and the initial anti-virus strength, which means the virus in the network can be controlled or eliminated in finite time by increasing the anti-virus strength. Finally, two illustrative examples are also given to support the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigate the problem of controlling chaos in a chaotic chemical system. The feedback method is used to suppress chaos to unstable equilibria or unstable periodic orbits. The Routh–Hurwitz criteria is applied to analyze the conditions of the asymptotic stability of the positive equilibrium. By choosing the delay as bifurcation parameter, we investigate what effect the delay has on the dynamics of the chemical system with delayed feedback. It is shown that the positive equilibrium is locally asymptotically stable when the time delay is sufficiently small, as the time delay passes through a sequence of critical values, then the positive equilibrium will lose its stability and a bifurcating periodic solution will occur. By using the normal form theory and center manifold argument, we derive the explicit formulae for determining the stability, the direction and the period of bifurcating periodic solutions. Finally, numerical simulation is provided to show the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]