  A method for certifying exact input trackability for constrained discrete
time linear systems is introduced in this paper. A signal is assumed to be
drawn from a reference set and the system must track this signal with a linear
combination of its inputs. Using methods inspired from robust model predictive
control, the proposed approach certifies the ability of a system to track any
reference drawn from a polytopic set on a finite time horizon by solving a
linear program. Optimization over a parameterization of the set of reference
signals is discussed, and particular instances of parameterization of this set
that result in a convex program are identified, allowing one to find the
largest set of trackable signals of some class. Infinite horizon feasibility of
the methods proposed is obtained through use of invariant sets, and an implicit
description of such an invariant set is proposed. These results are tailored
for the application of power consumption tracking for loads, where the operator
of the load needs to certify in advance his ability to fulfill some requirement
set by the network operator. An example of a building heating system
illustrates the results.
