Nonfragile robust [formula omitted] containment control for multi-agent systems with a time-varying delay

Abstract

Under a fixed directed graph, this paper is concerned with the distributed nonfragile robust H∞ containment control of linear multi-agent systems with model uncertainty subject to admissible external disturbances in the presence of communication delay. Compared with the situation where the controller only considers either nonfragility or time delay, a class of controller considering both nonfragility and time-varying communication delay is put forth while guaranteeing a prescribed H∞ performance level, under which all of the followers’ states merge into the convex hull created by those of the leaders. Specially, the nonfragile term is constructed to eliminate the inaccuracy and perturbation in the designing of the controller gain, where the additional tuning of parameters in the real control systems always occurs. Then, a four-term Lyapunov–Krasovskii functional is employed and analyzed, and a feasible methodology is designed to properly select the controller and observer gains depending on matrix transformation and solving linear matrix inequality. Finally, two simulation examples are used to demonstrate the viability of the proposed techniques.