Memory-Based PI-Type Sampled-Data Consensus Control for Nonlinear Multiagent Systems with Time-Varying Delays

In this paper, the sampled-data consensus problem of nonlinear multiagent systems (MASs) with time-varying delays is investigated. Compared with the widely used sampled-data controller, a proportional integral type (PI-type) protocol utilizing the information of neighbors considering the effects of memory delay is adopted. Then, by adequately considering characteristic about the time-varying delays, an improved time-varying quadratic type of Lyapunov-Krasovskii functional (LKF) is developed. Besides, augmented state vectors and two-sided looped-functional approach are adopting to constructed the LKF, some relaxed matrices in the LKF are not necessarily positive definite. Furthermore, some sufficient criteria are derived to ensure the consistency of the MASs. By solving a series of linear matrix inequalities, the desired memory PI-type sampled-data control gain matrices are obtained. Finally, the numerical examples are presented to illustrate the theoretical results.