Leader-following formation control of multi-agent systems in fixed and switching directed networks with time-varying delays

This paper is concerned with leader-following formation problem for second-order multi-agent systems. A modified neighbor-based formation control algorithm with time-varying is constructed. Employing Lyapunov-Razumikhin theorem and linear matrix inequalities (LMIs) approach, respectively, the formation consensus conditions are derived to guarantee the agents achieve and maintain the desired formation in a fixed directed network. Moreover, LMIs approach for a fixed directed network can be extended straightforwardly to switching directed networks. Finally, a numerical example is given to illustrate the effectiveness of the proposed results.