Finite-time lag consensus and finite-time H_∞ lag consensus for nonlinear multi-agent systems under communication delay

In this research, the finite-time lag consensus (FTLC) and finite-time H_∞ lag consensus (FTHLC) problems for first-order multi-agent systems (MASs) are studied. On the one hand, a new state feedback controller considering the communication delay between agents is proposed. Besides, based on several inequality scaling techniques and finite-time stability theory, a sufficient criterion is derived to guarantee the FTLC of MASs. On the other hand, an adaptive state feedback controller and the corresponding adaptive law are put forward, which can also help MASs realize lag consensus in finite time without any additional conditions. Moreover, to address inevitable external disturbances in practice, the proposed control strategies are further enhanced to achieve FTHLC, which further expands the application range of the research results. Finally, the effectiveness of these provided FTLC and FTHLC control schemes in different scenarios is manifested through some numerical simulation examples.