Cooperative control for a class of upper-triangular nonlinear systems with unknown growth rates

This paper is concerned the cooperative control for a class of upper-triangular nonlinear systems with unknown growth rates under directed leader-followers type network topology. Different from existing results the growth rates are required to be known, we consider unknown growth rates in this paper, which is more practical and general. By introducing time-scaling coordinates, the original system is transformed into an equivalent one with a time gain. After that, a time-varying state-feedback controller is adopted. Then, by using the algebraic graph theory and mathematical analysis method, it is proved that the followers can achieve bounded output tracking of the leader while keeping all the states of the closed-loop system bounded. Finally, a simulation example is given to verify the effectiveness of the proposed method.