Robust Guaranteed Cost Consensus for High-order Discrete-time Multi-agent Systems With Switching Topologies and Time Delays

The robust guaranteed cost consensus problem for high-order discrete-time linear multi-agent systems with parameter uncertainties is studied, under the condition of jointly-connected interconnections and time-varying delays. A corresponding linear consensus protocol design is proposed. The idea of robust guaranteed cost control is introduced to the consensus problem. After that, a cost function is defined based on the state errors among neighboring agents and control inputs of all the agents. By constructing a suitable Lyapunov function and using the stability theory of discrete-time linear systems, a sufficient linear matrix inequality (LMI) condition, as well as an upper bound of the cost function, is derived to ensure the robust guaranteed cost consensus of the concerned systems. Then, convergence results are provided as final consensus values for the high-order discrete-time linear multi-agent systems with switching topologies and time-varying delays. Numerical experiment is carried out to demonstrate the correctness and effectiveness of the theoretical results. Copyright © 2019 Acta Automatica Sinica. All rights reserved.