Global null controllability of perturbed linear systems with constrained controls (Q1119214)

The author provides sufficient conditions of global null controllability for systems of the type \(\dot x=(A+V(t))x+(B+B(t))u\). He assumes that the autonomous system \(\dot x=Ax+Bu\) is globally null controllable and he looks for conditions on the perturbations V(t) and B(t) which ensure that the property is preserved. Both the class of constrained and unconstrained controls are considered. The constrains on the controls are or on the values that the controls assume or on the \(L_ 1\) norm of the controls.