Finite‐time stability of singular multi‐agent systems with input time‐varying delay and non‐linear dynamics via non‐fragile controller
ChaoYu Xia, Chao Li Wang, Lin Li · The Journal of Engineering · 2022
Abstract This paper deals with the finite‐time stability problem of non‐linear singular multi‐agent systems subject to controller gain disturbance via a distributed non‐fragile controller. The existing literature on this problem only applies to normal multi‐agent systems, or ignores the possible change of control gain in the practical application of the controller, or requires that there is no time‐varying delay in the control input. How to tackle the finite‐time stability problem of singular multi‐agent systems by considering input time‐varying delay, Lipschitz non‐linear dynamics and controller gain perturbation simultaneously is an open issue. In order to solve this problem, a distributed non‐fragile controller is proposed for each agent to make the finite‐time stability problem solved for any connected undirected connection topology. With the help of a Linear matrix inequality and a Lyapunov integral appropriate expression, the difficulty caused by the irreversibility of singular system matrices is solved. Then, a sufficient condition to ensure the finite‐time stability of the closed‐loop system is obtained for the singular multi‐agent system including controller disturbance, input–output delay and non‐linear dynamics. Finally, two numerical examples are used to illustrate the effectiveness of the proposed method.