High-order tracking problem with a time-varying topology and communication delays

In this paper, tracking problem for high-order agents under uncertain communication topology and time varying delays is investigated. Each tracking agent is assumed only its own and neighbors׳ information is used in their tracking strategy design. The uncertain communication topology is modelled by a finite number of Laplacian matrices with their corresponding scheduling functions. Sufficient conditions for the existence of a tracking strategy have been expressed in terms of the solvability of linear matrix inequalities. Finally, numerical examples are given to verify the effectiveness and advantages of proposed tracking strategy. Through a set of simulations with various control parameters γ, the relationship between γ and the maximum allowable communications delays is tabulated.