# Leader-following consensus of discrete-time linear multi-agent systems with communication noises

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**Authors: **Wang, Y., Cheng, L., Wang, H., Hou, Z.G., Tan, M. and Yu, H.

**Journal:** Chinese Control Conference, CCC

**Volume:** 2015-September

**Pages:** 7010-7015

**eISSN:** 2161-2927

**ISBN:** 9789881563897

**ISSN:** 1934-1768

**DOI:** 10.1109/ChiCC.2015.7260748

© 2015 Technical Committee on Control Theory, Chinese Association of Automation. This paper studies the leader-following consensus problem of discrete-time generic linear multi-agent systems. Agents share their states with their neighbors via a noisy communication network. An algorithm is proposed for the leader-following consensus problem where the time-varying gain is employed to attenuate noises. Different from most previous results where all agents have to use the same time-varying gain, each agent can have its own time-varying gain. Sufficient conditions for solving the mean square leader-following consensus problem are obtained: 1) the communication topology graph has a spanning tree; 2) the summation of every time-varying gain from zero to infinite is infinite; 3) all time-varying gains are infinitesimal of the same order as time goes to infinity; and 4) all roots of a so-called 'parameter polynomial' are inside the unit circle. Finally, a simulation example is given to verify the theoretical results.