  This paper addresses the leader-following consensus problem for discrete-time
positive multi-agent systems over time-varying graphs. We assume that the
followers may have mutually different positive dynamics which can also be
different from the leader. Compared with most existing positive consensus works
for homogeneous multi-agent systems, the formulated problem is more general and
challenging due to the interplay between the positivity requirement and
high-order heterogeneous dynamics. To solve the problem, we present an extended
version of existing observer-based design for positive multi-agent systems. By
virtue of the common quadratic Lyapunov function technique, we show the
followers will maintain their state variables in the positive orthant and
finally achieve an output consensus specified by the leader. A numerical
example is used to verify the efficacy of our algorithms.
