Algebraic solution to distributed H2 control of multi-agent systems with time delays

This work deals with the problem of designing distributed controllers to improve consensus performance for identical dynamically coupled agents with time delays. Firstly, an H₂ optimization problem of the whole multi-agent systems is formulated. The decomposition approach is utilized to simplify the minimization of H₂ performance index to a set of independent optimization problems. For each decomposed subsystem, it is accomplished by an effective parametrization of all stabilizing controllers, which can be used to compute the H₂ optimal controller. Finally, the controllers with the same structure are obtained to achieve the performance improvement of the whole systems. The advantages of the proposed approach are that the design procedure is conducted analytically and a simple quantitative tuning way is developed to trade off the nominal performance and robustness. The simulation results show the effectiveness of this method.