Consensus Control and Optimization of Time-Delayed Multiagent Systems: Analysis on Different Order-Reduction Methods

This article addresses the consensus control and optimization issue for multiagent systems (MASs) with time-varying delay. Different from existing ones, an order-reduction method (ORM) is proposed to reduce the order of linear matrix inequalities (LMIs) without a complicated calculation process. The problem of complexity explosion caused by using LMI to analyze MASs is solved. To start with, we discuss and compare the existing ORMs and our ORM, respectively. Subsequently, under this improved ORM and the quadratic-delay-product method, a modified Lyapunov-Krasovskii functional (LKF) is constructed to obtain a less conservative consensus criterion. Then, we put forward a consensus controller which allows larger time delay upper bound. In addition, based on the self-adaptive differential evolution (DE) algorithm, the performance of the controller is significantly optimized. It is strictly proved that the designed controller can guarantee the realization of consensus and the LMI method used is feasible because it is independent of the number of agents. Finally, the simulation and comparison results illustrate the superiority of the theoretical results over others.