  In this paper, we study the conditions to be satisfied by a discrete-time
linear system to ensure output controllability using sparse control inputs. A
set of necessary and sufficient conditions can be directly obtained by
extending the Kalman rank test for output controllability. However, the
verification of these conditions is computationally heavy due to their
combinatorial nature. Therefore, we derive non-combinatorial conditions for
output sparse controllability which can be verified with polynomial time
complexity. Our results also provide bounds on the minimum sparsity level
required to ensure output controllability of the system. This additional
insight is useful for designing sparse control input that drives the system to
any desired output.
