Consensus control laws with guaranteed performance in presence of fixed delays

This paper deals with the design of optimal consensus control laws for a set of identical first and second order agents. Delayed versions of the relative states with respect to neighbours is used in the proposed consensus laws. Two different approaches are adopted: (i) assuming no delay is present in the exchange of information, design an optimal consensus law and for those gains, determine the maximum bound on the acceptable delay before stability deteriorates (ii) develop optimal consensus laws using a novel algorithm which explicitly accounts for a known fixed delay at the time of design itself. Optimal designs for a network of first and second order agents obtained using the two different approaches.