Dynamic consensus of nonlinear time-delay multi-agent systems with input saturation: an impulsive control algorithm

This paper aims to solve the dynamic consensus problem for a class of nonlinear multi-agent systems with input saturation and time delay. Due to the existing nonlinearity of the system, the low-gain feedback method widely used to handle saturation in multi-agent systems is no longer applicable. Moreover, to reduce both the communication and control energy consumption, an impulsive control algorithm is designed. Based on the stability theory of impulsive systems, as well as the property of the Laplacian matrix and convex hull, the set invariance conditions in the format of LMI are obtained. In addition, an optimization method is proposed for simultaneously designing the control parameters and assessing the attraction domain. Finally, the performance of the proposed consensus algorithms is demonstrated by two numerical experiments.