Finite-Time Consensus and Finite-Time $H_{\infty }$ Consensus of Multi-Agent Systems Under Directed Topology

Abstract

In this paper, we respectively discuss the finite-time consensus (FTC) and finite-time $H_{\infty }$ consensus (FTHC) problems for a kind of nonlinear multi-agent systems under directed topology. Firstly, with the help of some inequality techniques and the designed state feedback controller, a FTC criterion is presented for multi-agent system. In addition, two adaptive control strategies for ensuring the FTC of multi-agent system are also developed. Moreover, we further discuss the FTHC for multi-agent system with external disturbances, and some FTHC criteria are given by exploiting the designed state feedback controller and adaptive state feedback controllers. Finally, the effectiveness of these obtained results are verified by two numerical examples.