Output Controllability of a Linear Dynamical System With Sparse Controls

In this article, 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 noncombinatorial conditions for output sparse controllability that 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.

Automated summary

In this article, the conditions for a discrete-time linear system to achieve output controllability using sparse control inputs are studied. Necessary and sufficient conditions are obtained by extending the Kalman rank test, but their verification is computationally heavy due to combinatorial nature. Noncombinatorial conditions with polynomial time complexity are derived to verify output sparse controllability. The results also provide bounds on the minimum sparsity level required to ensure output controllability of the system.