Sliding Mode Consensus Control for Discrete-time Multi-agent Systems Under Markov Switching Topologies
The mean-square leader-following consensus problem for discrete-time multi-agent systems with the Mark-ovian switching topologies was studied by the sliding mode control.The Markovian switching topologies were introduced to describe the random information interaction between agents.The sliding mode surface with respect to the stochastic switc-hing topologies was constructed utilizing the consensus error.An equivalent controller was obtained according to the ideal quasi-sliding mode condition,and then the consensus problem of discrete-time multi-agent systems was transformed into the stability problem of leader-following error systems.A sufficient condition of the mean-square leader-following consensus was obtained for discrete-time sliding mode dynamics by the construction of Lyapunov function and the matrix theory,and the controller gains were designed.Then a discrete-time sliding mode controller was derived by using the reaching law principle to ensure that the following errors reached the area of the giving sliding mode surface in a finite time.How to deal with the Markov switching topologies with unknown partial transition probabilities and the design of sliding surface associated with stochastic switching topologies are two difficulties.Finally,a numerical example was given to illustrate the feasibility of the proposed method.
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