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Mathematical Problems in Engineering
Volume 2015, Article ID 453072, 13 pages
Research Article

Consensus of Noisy Multiagent Systems with Markovian Switching Topologies and Time-Varying Delays

Department of Mathematics, Tongji University, Shanghai 200092, China

Received 25 March 2015; Revised 26 May 2015; Accepted 21 July 2015

Academic Editor: Son Nguyen

Copyright © 2015 Yilun Shang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Stochastic multiagent systems have attracted much attention during the past few decades. This paper concerns the continuous-time consensus of a network of agents under directed switching communication topologies governed by a time-homogeneous Markovian process. The agent dynamics are described by linear time-invariant systems, with random noises as well as time-varying delays. Two types of network-induced delays are considered, namely, delays affecting only the output of the agents’ neighbors and delays affecting both the agents’ own output and the output of their neighbors. We present necessary and sufficient consensus conditions for these two classes of multiagent systems, respectively. The design method of consensus gains allows for decoupling the design problem from the graph properties. Numerical simulations are implemented to test the effectiveness of our obtained results as well as the tightness of necessary/sufficient conditions.