Controllability of Linear Dynamical Systems Under Input Sparsity Constraints

In this article, we consider the controllability of a discrete-time linear dynamical system with sparse control inputs. Sparsity constraints on input arises naturally in networked systems, where activating each variable adds to cost control. We derive algebraic necessary and sufficient conditions for ensuring an arbitrary transfer matrix. The derived can be verified polynomial time complexity, unlike more traditional Kalman-type rank tests. Further, characterize minimum number vectors required satisfy controllability. Finally, present generalized Kalman decomposition-like procedure that separates state-space into subspaces corresponding sparse-controllable sparse-uncontrollable parts. These results form theoretical basis designing systems