Stabilizability, Output Controllability, and Nonnegative Controllablity

This chapter builds upon the concept of sparse controllability and presents three related notions of controllability under input sparsity constraints:stabilizability, output controllability, and nonnegative controllability. We present three main results. We first prove that sparse stabilizability is equivalent to standard stabilizability. Next, we show that if a linear dynamical system is output controllable, there exist upper and lower bounds on the minimum sparsity level required to ensure sparse output controllability. Finally, we establish that a linear dynamical system is sparse nonnegative controllable if and only if it is both nonnegative controllable and sparse controllable.