Consensus in multi-agent systems with random delays governed by a Markov chain |
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Authors: | Jian Wu Yang Shi |
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Affiliation: | Department of Mechanical Engineering, University of Victoria, PO Box 3055, STN. CSC, Victoria, BC, V8W 3P6, Canada |
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Abstract: | This paper investigates the consensus problem in a multi-agent system with random delays governed by a Markov chain. The communication topology is assumed to be directed and fixed. With first-order dynamics under the sampled-data setting, we first convert the original system into a reduced-order one featuring the error dynamics. Accordingly, the consensus problem is transformed into the stabilization of the error dynamic system. Thereafter, based on the theory in stochastic stability for time-delay systems, a sufficient condition is established in terms of a set of linear matrix inequalities (LMIs). The mean square stability of the error dynamics is shown to guarantee consensus of the multi-agent system. By explicitly incorporating the transition probability of the random delay into consideration, the conservativeness in control design is reduced. A delay-dependent switching control scheme is developed by redesigning the adjacency matrix. Finally, simulation results are provided to verify the effectiveness of the proposed approach. |
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Keywords: | Multi-agent system Consensus Random delay Markov chain Mean square stability LMI Delay-dependent switching control |
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