# American Institute of Mathematical Sciences

December  2020, 25(12): 4535-4551. doi: 10.3934/dcdsb.2020111

## Consensus in discrete-time multi-agent systems with uncertain topologies and random delays governed by a Markov chain

 1 School of Management, Tianjin University of Technology, Tianjin 300384, China 2 Department of Basic Education, Tianjin City Vocational College, Tianjin 300250, China

* Corresponding author: Xi Zhu

Received  April 2019 Revised  October 2019 Published  March 2020

Fund Project: The first author is supported by the National Natural Science Foundation of China grant 61440058, 11501412 and 11401073

In this paper, we study consensus problem in a discrete-time multi-agent system with uncertain topologies and random delays governed by a Markov chain. The communication topology is assumed to be directed but interrupted by system uncertainties. Furthermore, the system delays are modeled by a Markov chain. We first use a reduced-order system featuring the error dynamics to transform the consensus problem of the original one into the stabilization of the error dynamic system. By using the linear matrix inequality method and the stability theory in stochastic systems with time-delay, several sufficient conditions are established for the mean square stability of the error dynamics which guarantees consensus. By redesigning its adjacency matrices, we develop a switching control scheme which is delay-dependent. Finally, simulation results are worked out to illustrate the theoretical results.

Citation: Xi Zhu, Meixia Li, Chunfa Li. Consensus in discrete-time multi-agent systems with uncertain topologies and random delays governed by a Markov chain. Discrete & Continuous Dynamical Systems - B, 2020, 25 (12) : 4535-4551. doi: 10.3934/dcdsb.2020111
##### References:

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##### References:
Communication topology with a directed spanning tree
Time delay ($d_k$) over time
State of all nodes in the original system
State of all nodes under the control scheme in [18] when $\alpha_0 = 0.26$
Consensus with switching adjacency matrices when $\alpha_0 = 0.26$
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