This paper studies the consensus problem of muti-agent systems with identical linear invariant dynamics. Both with and without a leader situation are considered. The controllers are designed with static relative output feedback. The communication topology is assumed to be fixed and contain a directed spanning tree. An optimal design method is introduced to design feedback gain so that the system can converge to the consensus value with a prescribed convergence speed.
I. INTRODUCTIONRecently, consensus problem of muti-agent systems has draw great attention for its broad potential applications in many areas such as cooperative control of vehicles[1,2] unmanned air vehicle formation [3][4][5]and flocking control [6,7]. It has been studies from different perspectives and many results have been got from different view points.In [8][9][10][11][12], consensus protocols were designed for first-order and second-order integral dynamics. High-order integral systems were studied in the articles [13][14][15]. The consensus problems of the general linear invariant dynamics which consider first-order and second-order integral dynamics as a special situation were studied in the recent works [1,[16][17][18][19][20][21][22]. In these papers, the consensus protocols were mostly designed with the neighbor's states or output as the feedback information. Different methods were used to design the consensus protocols. In [8,13,17,[23][24][25], the static state or output feedback was used to design the controllers. Dynamic feedback controllers were proposed in [23][24][25]. [17,26] proposed an observer-type consensus protocol with fixed communication topology which contains a directed spanning tree and the consensus regions were analyzed. In[17], tracking consensus problem was solved by optimal design method. Several protocols were proposed with static and dynamic state feedback. Unbounded synchronization regions were proposed. In [18], the consensusability of the multi-agent systems was studied with the communication topology contain a spanning tree. Necessary and sufficient conditions were proposed when the dynamics were both stabilizable and detectable. Many other control methods had been used to design the consensus protocols such as internal model principle [22,[27][28][29][30]. More consensus problems could be founded in the survey papers [11,31,32].