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multi-agent system; time delay system; robust control; LMI
The paper presents an algorithm for the solution of the consensus problem of a linear multi-agent system composed of identical agents. The control of the agents is delayed, however, these delays are, in general, not equal in all agents. The control algorithm design is based on the $H_\infty$-control, the results are formulated by means of linear matrix inequalities. The dimension of the resulting convex optimization problem is proportional to the dimension of one agent only but does not depend on the number of agents, hence this problem is computationally tractable. It is shown that heterogeneity of the delays in the control loop can cause a steady error in the synchronization. Magnitude of this error is estimated. The results are illustrated by two examples.
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