Null controllability of linear systems with control restraints

This paper provides some necessary conditions and some sufficient conditions for the null controllability of constant linear systems and a class of time-varying linear systems. The approach provides geometrical interpretations of the usual algebraic criteria and gives insight into the effects of restrained controls. The results show that controllability of a linear system imposes relationships among the cyclic subspaces (algebraic structure of the system), the eigenvalues, and the control restraint set.