Null controllability in function space of nonlinear retarded systems with limited control (Q761386)

The main result is such that the system with limited control \[ \dot x(t)=\int^{0}_{-h}d_ s\eta (t,s)x(t+s)+B(t)u(t),\quad u(t)\in U,\quad 0\in int U, \] is null controllable if it is complete and the free system is uniformly asymptotically stable. The result is applied to the investigation of nonlinear functional-differential systems with limited control.