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∞-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.
This papers extends the Inclusion Principle to a class of linear continuous-time uncertain systems with state as well as control delays. The derived expansion-contraction relations include norm bounded arbitrarily time-varying real uncertainties and a point delay. They are easily applicable also to polytopic uncertainties. These structural conditions are further specialized on closed-loop systems with arbitrarily time-varying parameters, a point delay, and guaranteed quadratic costs. A linear matrix inequality (LMI) delay independent procedure is used for control design in the expanded space. The results are specialized on the overlapping decentralized control design. A numerical illustrative example is supplied.