The study is motivated by the problem of stabilizing the concentration of atmospheric carbon, which is widely discussed in the context of global warming nowadays. A key difficulty in the design of stabilization strategies is the uncertainty of the underlying physical model. In the present paper, a general problem setting is suggested and a relevant alanytic framework elaborated. Analysis employs specific qualitative features of an uncertain dynamics, including automatic stabilization of the trajectories in the absence of input disturbances. An asymptotic version of Krasovskii's extremal shift control principle is developed and model-robust strategies stabilizing a state coordinate at a prescribed level are constructed.