Distributed reduced-order observer-based approach to consensus problems for linear multi-agent systems

In this study, the authors probe the multi-agent consensus problem with general linear dynamics via the distributed reduced-order observer-based protocols under directed switching topology. A new type reduced-order observer is adopted to modify the existed consensus protocols. Based on graph theory, Riccati equation and Lyapunov method, a multi-step algorithm is provided to design the gain matrices involved in the used protocols. The consensus stability problem is investigated by use of the piecewise Lyapunov functions incorporated with an average dwell time approach. It is shown that if the average dwell time is chosen sufficiently large and all directed switching topologies have a directed spanning tree, then the multi-agent system can achieve consensus via the author´s modified protocols. Furthermore, as the special cases, the consensus conditions under fixed topology and balanced switching topology are obtained easily. To obtain a desired consensus decay rate, the related gain matrix design approach is provided. Finally, a simulation example is given to illustrate the effectiveness of their obtained results.