This paper is devoted to the leader–follower consensus problem for high-order multi-agent systems with inherent nonlinear dynamics evolving on an arbitrary time domain. This problem is investigated using the time scale theory. Based on this theory, some sufficient conditions are derived to guarantee that the tracking errors exponentially converge to zero using the concept of matrix-valued Lyapunov functions when directed interaction topology is considered. An academic example is given to illustrate the pertinence and the feasibility of the theoretical results.