A class of cooperative relay analysis of multi-agent systems with tracking number switching and time delays. (July 2019) - Dong, Lijing
Abstract: This paper investigates a complicated class of cooperative tracking problems with time-varying number of tracking agents and communication time delays. During the entire tracking process, tracking agents are dynamically changing and the number is not fixed. This results in jumping of tracking errors and dynamic dimensions of the corresponding Laplacian matrices. Consequently, the stability analysis turns to be difficult especially when the effect of communication time delays is taken into consideration. In order to solve this issue, a new type of average Lyapunov function is constructed to compensate the unmatched dimensions of communication topologies over different time intervals. Generalized reciprocally convex Lemma and a more relaxed switched technique are employed to achieve a less conservative switched stability condition for the multi-agent system with variable tracking number and time delays. Finally, through a series of numerical simulations, the effectiveness and feasibility of derived results are verified. The relationship between maximum allowable communication time delays and various control parameters is obtained in a quantitative way. Highlights: No strict requirement to the number of tracking agents during the whole tracking process. A newtype of average Lyapunov function is constructed to compensate the unmatch dimension of communication topology. A less conservative switched stability condition for the multi-agent system with variable tracking number and time delays is achieved.