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Stabilization strategies of supply networks with stochastic switched topology. (English) Zbl 1271.93121

Summary: In this paper, a dynamical supply networks model with stochastic switched topology is presented, in which the stochastic switched topology is dependent on a continuous time Markov process. The goal is to design the state-feedback control strategies to stabilize the dynamical supply networks. Based on Lyapunov stability theory, sufficient conditions for the existence of state feedback control strategies are given in terms of matrix inequalities, which ensure the robust stability of the supply networks at the stationary states and a prescribed \(H_\infty\) disturbance attenuation level with respect to the uncertain demand. A numerical example is given to illustrate the effectiveness of the proposed method.

MSC:

93D15 Stabilization of systems by feedback
90B15 Stochastic network models in operations research
93B36 \(H^\infty\)-control
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