On controllability of nonlinear systems with distributed delays in the control (Q1115828)

It is known that most natural applications give rise to mechanisms of indirect actions, where the decisions in the control function u are shifted, twisted or combined before effecting the evolution. An example of this delayed action is the model defined by \[ \dot x(t)=g(t,x(t),u(t))+\int^{0}_{-h}(d_ sB(t,s))u(t+s). \] We give sufficient conditions for the null controllability of such systems when the controls are limited in the sense that they lie in a closed unit ball with zero in its interior. These extend known results.