An algebraic approach to bounded controllability of linear systems†

In this paper we present an algebraic approach to the proof that a linear system with matrices (A, B) is null–controllable using bounded inputs if and only if it is null–controllable (with unbounded inputs) and all eigenvalues of A have non–positive real parts (continuous time) or magnitude not greater than one (discrete time). We also give the analogous results for the asymptotic case. Finally, we give an interpretation of these results in the context of local non–linear controllability.