Resumen
In this paper, for multi-agent systems (MASs) with leader-follower structures, we present a linear matrix inequality (LMI)-based design method of an adaptive gain controller considering relative distances between agents. The proposed adaptive gain controller consists of fixed gains and variable ones tuned by time-varying adjustable parameters. The objective of this paper is to derive enough conditions for the existence of the proposed adaptive gain controller which achieves consensus for each agent. The advantages of the proposed adaptive gain controller are as follows; The proposed controller can be obtained by solving LMI, and the proposed control system can achieve consensus and formation control, even if uncertainties are included in the information for relative distances. In this paper, we show that the design problem of the proposed adaptive gain controller can be reduced to the solvability of LMI. Finally, simple numerical examples are included to illustrate the effectiveness of the proposed adaptive gain controller for MASs.